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1227455-1322414MAP to Khan Academy:Khan Academy Practice Exercises Correlated to RIT for Common Core Math MAP Grades 6+ 0MAP to Khan Academy:Khan Academy Practice Exercises Correlated to RIT for Common Core Math MAP Grades 6+ About this DocumentThis document correlates MAP? sub-goals and RIT ranges to Khan Academy? exercises. The Khan exercises are interactive problems for students with instant feedback:Having these exercises correlated to RIT ranges means you can use them in conjunction with your flexible student groupings that are also informed by RIT score results. The exercises are also useful for targeting learning in each student’s zone of proximal development (Vygotsky).The correlation between MAP RIT scores and the Khan Academy exercises was determined by using our 2011 norms data to approximate grade levels, which were then matched to the corresponding Common Core State Standards (CCSS). Teachers in states that have not adopted the CCSS may still find these resources valuable by relating goals or sub-goals that are similar to CCSS goals and sub- goals.NWEA plans to work with Khan Academy to update these links twice a year as new exercises are developed.How to UseUse MAP reports to find the RIT scores for a given sub-goal.In this document, locate that same goal, approximate RIT range, and sub-goals.To choose appropriate Khan Academy exercises:Consider both the name of the exercise and the CCSS standard.Click the link and try the exercise yourself.Note: When you’re in Khan Academy, the links to videos and other resources add context to the actual exercise but are not necessarily correlated to MAP.In the browser window where the exercise opened, note or copy the Web address URL.Optionally deliver exercises to students. For example:Paste the URL into an online document for students to access.Present the exercise in the classroom.Use for parent-teacher conference discussion.LimitationsThe instructional suggestions presented in this document are intended to provide supplementary resources based on available Khan Academy exercises and are not intended to replace other options. MAP/MPG data should be used as one of many data points for instructional decisions rather than as a placement guide.Terms of UseThese Terms of Use permit you to use this document for your personal, non-commercial use only. You must not reproduce, distribute, modify, create derivative works of, publicly display, publicly perform, republish, download, store or transmit any of the material on this document, except you may print or download one copy of a reasonable number of pages of this document for your own personal, non-commercial use and not for further reproduction, publication or distribution. You must not modify copies of this document. You must not delete or alter any copyright, trademark or other proprietary rights notices from this document. If you breach the Terms of Use your right to use the document will cease immediately and you must, at NWEA’s option, return or destroy any copies of the document you have made. No right, title or interest in or to the document or any content on the document is transferred to you, and all rights not expressly granted are reserved by NWEA or their respective owner (see below). Any use of the document not expressly permitted by these Terms of Use is a breach of these Terms of Use and may violate copyright, trademark and other laws.This document contains links to Khan Academy? sites, materials and/or resources (“Khan Materials”). NWEA’s use of the Khan Materials is by license. Khan Academy? is the respective owner of the Khan Materials. NWEA’s use of the Khan Materials in no way represents or suggests that Khan Academy? endorses NWEA. All Khan Academy content is available for free at .The Khan Materials are provided for your convenience only. NWEA has no control over the contents of the Khan Materials and accepts no responsibility for them or for any loss or damage that may arise from your use of them. The information contained in this document, including the Khan Materials, are provided “as-is” and “as available” without any warranty of any kind, express or implied. NWEA does not warrant the accuracy, completeness or usefulness of the Khan Materials or any other information in this document and NWEA expressly disclaims all liability and responsibility arising from any reliance placed on the Khan Materials and/or any other information in this document. If you decide to access any of the Khan Materials, you do so entirely at your own risk and subject to the terms and conditions of use for the Khan Materials.NWEA disclaims all warranties of any kind, whether express or implied, statutory or otherwise, including but not limited to any warranties of merchantability, non-infringement and fitness for particular purpose. In no event will NWEA be liable for damages of any kind, under any legal theory, arising out of or in connection with your use, or inability to use, this document and/or the information contained within it, including any direct, indirect, special, consequential, incidental or punitive damages. Any dispute or claim arising from or related to this document shall be governed and construed with the laws of the State or Oregon and any suit or action arising out of this document shall be instituted exclusively in the court of the State of Oregon and County of Multnomah.The Khan Academy? is a registered trademark of Khan Academy. MAP? is a registered trademark of Northwest Evaluation Association. You must not use such marks without the prior written permission of their respective owners. NWEA may update the content on this document from time to time, but its content is not necessarily complete or up-to-date. Any of the material in this document may be out of date at any given time, and NWEA is under no obligation to update such material. However, in the event NWEA, in its sole discretion updates this document, your continued use of it following the posting of revised Terms of Use means that you accept and agree to the mon Core MAP MathematicsKhan Academy Practice Exercises Correlation Common Core Mathematics 6+GeometryCongruence, Similarity, Right Triangles, & TrigP 4Geometric Measurement and RelationshipsP 6 Operations and Algebraic ThinkingExpressions and EquationsP 15Use Functions to Model RelationshipsP 32Statistics and ProbabilityInterpreting Categorical and Quantitative DataP 45Using Sampling and Probability to Make DecisionsP 50The Real and Complex Number SystemsExtend and Use PropertiesP 52Perform OperationsP 58Ratios and Proportional RelationshipsP 706+ | Geometry | Congruence, Similarity, Right Triangles, & Trig | RIT 204 - 212GeometryCongruence, Similarity, Right Triangles, & TrigStandards AlignmentRIT Range: 204 - 212Quadrilateral types4.G.A.2RIT Range: 203-212Draw and identify lines of symmetry. Create and identify symmetrical shapes.4.G.A.3Practice drawing lines of symmetry and creating symmetrical figures.4.G.A.3RIT Range: 226 - 230Vertical angles7.G.B.5RIT Range: 228-230Use your knowledge about angles to find missing angle measures in various situations.Use your knowledge about angles to find missing angle measures in various complex situations.Use the Pythagorean theorem to find the distance between two points on the coordinate plane.8.G.A.58.G.A.58.G.B.8Given two polygons, try to map one onto the other using angle-preserving 8.G.A.4 | HSG-SRT.A.2transformations, and determine whether they are similar. Transformations are done in "intuitive mode."Given a pair of figures in the coordinate plane, try to map one onto the other and determine whether they are congruent.8.G.A.2 | HSG-CO.B.6Find missing angles given two parallel lines and a transversal.8.G.A.5Equation practice with congruent angles8.G.A.5Use the interactive transformation tool to perform reflections.8.G.A.1 | 8.G.A.3 | HSG-CO.A.2 | HSG-CO.A.5 Use the interactive transformation tool to perform rotations.8.G.A.1 | 8.G.A.3 | HSG-CO.A.2 | HSG-CO.A.5 Use the interactive transformation tool to perform translations.8.G.A.1 | 8.G.A.3 | HSG-CO.A.2 | HSG-CO.A.5Find the leg or hypotenuse of a right triangle using the Pythagorean theorem.8.G.B.7Pythagorean theorem in 3D8.G.B.7Solve real-world problems that can be modeled by right triangles, using the 8.G.B.7 Pythagorean Theorem!RIT Range: > 23145021563436500Given a description of a sequence of transformations, determine whether it preserves segment length or angle measure.HSG-CO.A.56+ | Geometry | Congruence, Similarity, Right Triangles, & Trig | RIT > 231GeometryCongruence, Similarity, Right Triangles, & TrigStandards AlignmentRIT Range: > 231Solve word problems by modeling real-world (and not-so-real) situations as right triangles and using trigonometry.Use the triangle congruence criteria SSS, SAS, ASA, and AAS to determine that two triangles are congruent.Given two triangles, determine whether they are congruent and use that to find missing angle measures.Map a given shape to another one using rigid transformations and dilations. Determine whether the shapes are congruent.Find both the center and the scale factor of a dilation that maps a given figure to another one.HSG-SRT.C.8HSG-CO.C.10 | HSG-CO.C.11 | HSG-CO.C.9 HSG-CO.C.10HSG-CO.B.6HSG-SRT.A.1Given two figures on the coordinate plane, find the formal definition of the HSG-CO.A.2 | HSG-CO.A.5reflection that takes one figure to another.Given a figure on the coordinate plane and a center of a rotation, find the angle for the rotation that maps one figure to the other.HSG-CO.A.2 | HSG-CO.A.5Given two polygons, try to map one onto the other using angle-preserving HSG-SRT.A.2transformations, and determine whether they are similar. Transformations are done in "formal mode."Given two figures on the coordinate plane, find the formal definition of the HSG-CO.A.2 | HSG-CO.A.5translation that takes one figure to another.Given a figure and a definition of a dilation, manually draw the image.HSG-SRT.A.1Given two polygons, try to map one onto the other using angle-preserving 8.G.A.4 | HSG-SRT.A.2transformations, and determine whether they are similar. Transformations are done in "intuitive mode."Given a pair of figures in the coordinate plane, try to map one onto the other and determine whether they are congruent.8.G.A.2 | HSG-CO.B.6Find missing angles in isosceles triangles given just one angle.HSG-CO.C.10Geometric definitionsHSG-CO.A.1Explore different ways of proving some theorems about lines and angles. Some transformations are used.HSG-CO.C.9Use the interactive transformation tool to perform dilations.HSG-SRT.A.1Use the interactive transformation tool to perform reflections.8.G.A.1 | 8.G.A.3 | HSG-CO.A.2 | HSG-CO.A.5 Use the interactive transformation tool to perform rotations.8.G.A.1 | 8.G.A.3 | HSG-CO.A.2 | HSG-CO.A.5 Use the interactive transformation tool to perform translations.8.G.A.1 | 8.G.A.3 | HSG-CO.A.2 | HSG-CO.A.5Use your knowledge of 30-60-90 and 45-45-90 triangles to solve some problems.Given a description of the effect of a transformation, determine which rigid transformation it is.HSG-SRT.C.8HSG-CO.A.2 | HSG-CO.A.4Understand the right triangle definition of sec, csc, and cot ratios.HSG-SRT.C.66+ | Geometry | Congruence, Similarity, Right Triangles, & Trig | RIT > 231GeometryCongruence, Similarity, Right Triangles, & TrigStandards AlignmentRIT Range: > 231Given a figure and a definition of a reflection, manually draw the image.HSG-CO.A.5Find the reflection that maps a given figure to another and draw the image HSG-CO.A.5of a reflection. The lines of reflection in this exercise have a wide range of slopes.Given a figure on the coordinate plane and the definition of a rotation about the origin, manually draw the image of that rotation.Given a figure on the coordinate plane and the definition of a rotation about an arbitrary point, manually draw the image of that rotation.HSG-CO.A.5HSG-CO.A.5Given two triangles with some of their angle measures, determine whether HSG-SRT.A.2 | HSG-SRT.A.3the triangles are similar or not.Given two triangles with some of their side measures, determine whether the triangles are similar or not.Given two similar triangles and some of their side lengths, find a missing side length.Given two similar triangles and some of their side lengths, find a missing side length.Solve geometry problems with various polygons by using all you know about similarity and congruence.Analyze various shapes according to their reflective and rotational symmetries.HSG-SRT.A.2 | HSG-SRT.A.3HSG-SRT.B.5 HSG-SRT.B.5 HSG-SRT.B.5 HSG-CO.A.3Given a figure and a definition of a translation, manually draw the image.HSG-CO.A.5Find missing angle measures in triangles using the properties of general triangles, isosceles triangles, and equilateral triangles.HSG-CO.C.10DEPRECATED Trigonometry 0.5HSG-SRT.C.6Given the side lengths of a right triangle, find the sine, cosine, or tangent of HSG-SRT.C.6one of the acute angles.DEPRECATED Trigonometry 1.5HSG-SRT.C.6Given one side length and an acute angle in a right triangle, find another side using trigonometry.GeometryGeometric Measurement and RelationshipsHSG-SRT.C.6Standards AlignmentRIT Range: < 160Practice comparing shapes based on their number of sides, number of corners, and side-lengths.K.G.B.4Practice combining shapes to make other shapes.K.G.B.6Practice identifying circles, triangles, squares, and rectangles.K.G.A.16+ | Geometry | Geometric Measurement and Relationships | RIT 161-178GeometryGeometric Measurement and RelationshipsStandards AlignmentRIT Range: 161-178Practice identifying circles, triangles, squares, rectangles, rhombuses, trapezoids, and hexagons.1.G.A.1Compare the lengths of 2 objects indirectly by using a third object.1.MD.A.1 Measure objects with same-size length units without gaps or overlaps. 1.MD.A.2 Practice ordering 3 objects by length.1.MD.A.1RIT Range: 179-191Estimating lengths2.MD.A.3RIT Range: 179-191Add and subtract lengths to solve word problems.2.MD.B.5Measure objects using a ruler.2.MD.A.1Practice identifying quadrilaterals, pentagons, hexagons, and octagons.2.G.A.1RIT Range: 192 - 203Decompose shapes to find area3.MD.C.7Finding area by multiplying3.MD.C.7RIT Range: 192-202Comparing areas by multiplying3.MD.C.7bRIT Range: 192-202Compare the areas and perimeters of rectangles when given a context or picture.3.MD.D.8Practice estimating the mass of real life objects using grams and kilograms. 3.MD.A.2 Practice estimating the volume of real life objects using milliliters and liters. 3.MD.A.2 Find a missing side length for a figure when given the perimeter.3.MD.D.8Practice finding the area of rectangles by counting unit square. Create rectangles with a given area by covering unit squares.3.MD.C.6Solve word problems involving mass. Estimate the mass of items.3.MD.A.2 Practice measuring side lengths to find perimeter.3.MD.D.8 Count unit squares and partial unit squares to find the area of shapes. 3.MD.C.6 Calculate the perimeter of a shape from its side lengths.3.MD.D.86+ | Geometry | Geometric Measurement and Relationships | RIT 192-202GeometryGeometric Measurement and RelationshipsStandards AlignmentRIT Range: 192-202Find perimeter of figures when given an image or context.3.MD.D.8 Practice solving real world word problems involving perimeter.3.MD.D.8 Compare the amount of unit squares that cover figures.3.MD.C.5 Solve word problems involving volume. Estimate the volume of items. 3.MD.A.2RIT Range: 203-212Determine if an angle is acute, right, or obtuse. A protractor is provided. 4.G.A.1Find the area of rectangles and squares when given side lengths. Find the side length of a square when given the area.Find the missing side length of a rectangle when given its perimeter or area. Compare perimeters and areas of rectangles.Find the area of rectangles and squares when given side lengths. Find the side length of a square when given the area.4.MD.A.34.MD.A.34.MD.A.3Estimate the size of angles when given a picture or a situation.4.MD.C.5Classify shapes based on pictures or attributes, such as angle types and side-lengths. 4.G.A.2Practice converting a US customary measure of volume to a smaller unit. 4.MD.A.1 Practice converting a metric measure of mass to a smaller unit.4.MD.A.1 Practice converting a US customary measure of length to a smaller unit. 4.MD.A.1 Practice converting a metric measure of volume to a smaller unit.4.MD.A.1 Practice converting a metric measure of length to a smaller unit.4.MD.A.1 Practice converting a US customary measure of mass to a smaller unit. 4.MD.A.1 Find an angle's measure when given the measures of its parts.4.MD.C.7 Use a protractor to construct angles.4.MD.C.6Draw rays, lines, and line segments with given points.4.G.A.1 Practice drawing parallel and perpendicular lines, line segments, and ray.4.G.A.1 Create an acute, right, or obtuse angle using a given vertex.4.G.A.1 Practice estimating the length of real life objects using US customary units. 4.MD.A.1 Practice estimating the length of real life objects using metric units.4.MD.A.1 Practice estimating the mass of real life objects using US customary units.4.MD.A.1 Practice estimating the volume of real life objects using US customary4.MD.A.1 Practice identifying triangles by their angles as acute, right, or obtuse.4.G.A.26+ | Geometry | Geometric Measurement and Relationships | RIT 203-212GeometryGeometric Measurement and RelationshipsStandards AlignmentRIT Range: 203-212Practice converting a measure of time to a smaller unit.4.MD.A.1Measure angles using a protractor.4.MD.C.6Solve word problems that involve converting between U.S. dollars and cents and converting U.S. dollars to other units of money, like pesos. Solve word problems to find what time an event occurred or how long an event lasted.4.MD.A.24.MD.A.2Name angles by their vertex, endpoints, or labels.4.MD.C.5Identify quadrilaterals based on pictures or attributes. Quadrilaterals included are parallelograms, rhombuses, rectangles, and squares.4.G.A.2Determine if angles in shapes and pictures are acute, right, or obtuse.4.G.A.1 Recognize rays, lines, and line segments in geometric figures.4.G.A.1 Determine if angles in shapes and pictures are acute, right, or obtuse.4.G.A.1Recognize parallel and perpendicular lines in geometric figures and pictures. Practice identifying triangles by their side-lengths as equilateral, isosceles, or scalene.Practice estimating the length of an event using seconds, minutes, and hours.4.G.A.14.G.A.24.MD.A.1RIT Range: 213 - 220Converting measurements word problems5.MD.A.1Converting units5.MD.A.1RIT Range: 213-219Decompose figures to find volume5.MD.C.5 | 5.MD.C.5c91948024066500Volume 15.MD.C.5 | 5.MD.C.5b91948024003000Volume word problems5.MD.C.5 | 5.MD.C.5b | 5.MD.C.5cVolume with unit cubes 15.MD.C.4 | 5.MD.C.5Volume formula intuition5.MD.C.5RIT Range: 213-219Find the distance between points, graph points, and interpret data on coordinate planes to solve word problems.Graph and find the distance between point in first quadrant of coordinate plane.5.G.A.25.G.A.26+ | Geometry | Geometric Measurement and Relationships | RIT 213-219GeometryGeometric Measurement and RelationshipsStandards AlignmentRIT Range: 213-219Plot a given point on the coordinate plane.5.G.A.2Identify and compare shapes based on their attributes. Shapes include triangle types, quadrilateral types, pentagons, and hexagons.Identify and graph corners on shapes graphed in the first quadrant of a coordinate plane.5.G.B.35.G.A.2Recognize volume as an attribute of solid figures and understand concepts 5.MD.C.4of volume measurement.RIT Range: 220-223Practice finding the area of parallelograms given base and height.6.G.A.1Practice finding the area of right, acute, and obtuse triangles from a diagram.6.G.A.1Practice finding the areas of complex shapes that are composed of smaller 6.G.A.1shapes.Practice finding the areas of triangles and quadrilaterals on grids.6.G.A.1Practice finding the areas of trapezoids.6.G.A.1Practice solving problems involving triangles, parallelograms, and composite figures. Exercises include decimals, fractions, and word problems. Area of circles is not included.6.G.A.1Practice drawing shapes on the coordinate plane.6.G.A.3More challenging problems involving drawing shapes on the coordinate plane.6.G.A.3Practice matching 2D nets to the 3D shapes the fold up into.6.G.A.4Challenge problems involving the coordinates of the vertices of the quadrilaterals6.G.A.3Practice using the net of a 3D figure to find surface area.6.G.A.4Practice finding the surface area of 3D objects.6.G.A.4Practice finding the volume of rectangular prisms that have fractional side lengths.Practice solving volume word problems involving objects like fish tanks, truck beds, and refrigerators. 6.G.A.26.G.A.2RIT Range: 224-227Find the area of a circle given its radius, diameter, or circumference.7.G.B.4 Practice interesting area and circumference problems.7.G.B.4 Practice finding the area or circumference of part of a circle.7.G.B.46+ | Geometry | Geometric Measurement and Relationships | RIT 224-227GeometryGeometric Measurement and RelationshipsStandards AlignmentRIT Range: 224-227Use your knowledge about complementary and supplementary angles to find missing angles.7.G.B.5An urban planner needs your help in creating a scale drawing. Let's use our 7.G.A.1knowledge about scale factor, length, and area to assist.Practice constructing triangles.7.G.A.2Practice using knowledge of vertical, complementary, and supplementary angles to find a missing angle.7.G.B.5Practice telling whether two angles are supplementary, complementary, or 7.G.B.5 vertical.Interpreting scale drawings7.G.A.1Find missing angle measures in quadrilaterals.7.G.B.5Practice finding the radius, diameter, or circumference of a circle. For example, if the diameter of a circle is 16, what is its circumference?Find the areas of shaded regions which are combinations of squares, triangles, and circles. 7.G.B.47.G.B.6Match 3D objects with their 2D cross-sections.7.G.A.3Practice setting up algebraic equations to solve unknown angle problems.7.G.B.5Given the lengths of two sides of a triangle, what can we say about the third side?7.G.A.2Use your knowledge about vertical angles to find missing angle measures.7.G.B.5RIT Range: 228-230Find volumes and surface areas of boxes, cylinders, & triangular prisms.8.G.C.9Solve problems concerning real-world situations with the volumes of cones, cylinders, and spheres.8.G.C.9 | HSG-GMD.A.3RIT Range: > 231Use the fact that the arc measures of a circle must sum to 360 degrees to find missing arc measures.Use the fact that the arc measures of a circle must sum to 360 degrees to find missing arc measures by setting up equations.HSG-C.A.2HSG-C.A.2Relate the area of a sector to the area of a whole circle.HSG-C.B.5Solve problems related to radians and arc length like finding an arc length given the central angle and radius.HSG-C.B.5Solve problems related to tangents of circles.HSG-C.A.2 | HSG-C.A.3Relate the length of an arc to the circumference of a whole circle and the central angle subtended by the arc.HSG-C.B.56+ | Geometry | Geometric Measurement and Relationships | RIT > 231GeometryGeometric Measurement and RelationshipsStandards AlignmentRIT Range: > 231Given points that two lines go through or the graph of each line, classify the lines as parallel, perpendicular, or neither.Solve all sorts of word problems with crazy contexts that use polygons on the coordinate plane.Practice your knowledge of all possible cross-sections of common 3D objects.HSG-GPE.B.5 HSG-GPE.B.7 HSG-GMD.B.4Convert angle measures given in degrees to radians and vice versa.HSG-C.B.5Figure out the coordinates of a point between two other points that give a HSG-GPE.B.6certain ratio. For example, find a point C so that it is two thirds of the way between point A and B.Find the center and radius of a circle given the equation in standard form. HSG-GPE.A.1 Find the center and radius of a circle given the equation in expanded form. HSG-GPE.A.1 Given the focus and the directrix of a parabola, find its equation.HSG-GPE.A.2Find the area or perimeter of shapes like triangles, rectangles, parallelograms, and hexagons on the coordinate plane.HSG-GPE.B.7Given the graph of a circle, find its center and radius.HSG-GPE.A.1Given the center and radius of a circle, determine if a point is inside of the HSG-GPE.B.4circle, on the circle, or outside of the circleGiven information about the center and radius of a circle, graph it.HSG-GPE.A.1 Given the standard form equation of a circle, graph the circle.HSG-GPE.A.1 Given an expanded equation of a circle, graph it.HSG-GPE.A.1Practice the relationship between inscribed & central angles that are subtended by the same arc length.HSG-C.A.2Find missing angles and lengths in inscribed shapes.HSG-C.A.2Use the fact that opposite angles in an inscribed quadrilateral are supplementary to solve a few problems.HSG-C.A.3Given the equation of two lines in a variety of forms, determine if they are HSG-GPE.B.5equal, parallel, perpendicular, or neither.Find the midpoint of a segment on the coordinate plane, or find the endpoint of a segment given one point and the midpoint.HSG-GPE.B.6Practice your 3D visualization skills by rotating 2D shapes.HSG-GMD.B.4Solve problems concerning real-world situations using your knowledge of volume, surface area, and density.Solve problems concerning real-world situations with the volumes of cones, cylinders, and spheres.HSG-MG.A.28.G.C.9 | HSG-GMD.A.3Given the graph of a circle or its features, find its standard equation.HSG-GPE.A.16+ | Geometry | Geometric Measurement and Relationships | RIT > 231GeometryGeometric Measurement and RelationshipsStandards AlignmentRIT Range: > 231Write the equation for a line that is a parallel or perpendicular to a line given in slope-intercept form and goes through a specific point.Operations and Algebraic ThinkingExpressions and EquationsHSG-GPE.B.5Standards AlignmentRIT Range: < 160Practice adding by "putting together" (with numbers less than 10).K.OA.A.1Practice subtracting by "taking apart" (with numbers less than 10).K.OA.A.1RIT Range: 161-178Practice adding 3 numbers. All numbers in these problems are 20 or less.1.OA.A.2Practice adding and subtracting to solve word problems. Numbers used are 1.OA.A.1 20 or less.Practice solving more challenging word problems with addition and subtraction. Numbers used are 20 or less.Practice solving word problems by finding how many more (or fewer) objects there are. Numbers used are 20 or less.Practice solving more word problems by finding how many more (or fewer) objects there are. Numbers used are 20 or less.1.OA.A.11.OA.A.11.OA.A.191503517145000Learn how to solve problems like "_- 7 = 18" where you don't know one1.OA.D.8of the values in an addition or subtraction equation.Practice seeing how addition and subtraction are related.1.OA.B.4RIT Range: 179-191Practice adding and subtracting to solve word problems. These questions are result unknown or change unknown problems. Numbers used are 100 or less.Practice solving word problems with addition and subtraction. These questions are comparison problems including difference unknown, smaller value unknown, and bigger value unknown. Numbers used are 100 or less. Practice solving word problems with addition and subtraction. These questions are start unknown problems including add to and take from problems. Numbers used are 100 or less.2.OA.A.12.OA.A.12.OA.A.1Practice solving more challenging addition and subtraction word problems 2.OA.A.1with "more" and "fewer".€? Multi-step problems are also included. Numbers used are 100 or less.91503517081500Practice solving problems like "_- 45 = 27" where you have to figure out2.OA.A.1the missing value in an addition or subtraction equation.6+ | Operations and Algebraic Thinking | Expressions and Equations | RIT 179-191Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: 179-191Add and subtract lengths to solve word problems.2.OA.A.1Practice adding 2-digit numbers like 43+27 that have sums that are multiples of 10.2.NBT.B.5Practice adding two-digit numbers by making groups of ten.2.NBT.B.5Read and interpret picture graphs.2.OA.A.1RIT Range: 192-202Addition using groups of 10 and 1003.NBT.A.2RIT Range: 192-202Practice changing the grouping of factors in multiplication problems and see how it affects the product.Practice changing the order of factors in a multiplication problem and see how it affects the product.3.OA.B.53.OA.B.5Divide two numbers. Quotients are equal to or less than 10.3.OA.A.4 Practice solving for unknown letters and symbols in equations.3.OA.B.6 See the relationship between multiplication and division problems.3.OA.B.6Find both the multiplication and division equation that can be used to solve a word problem.Solve two-step word problems with addition, subtraction, multiplication, and division. Some questions include estimation. 3.OA.B.63.OA.D.8RIT Range: 204 - 212Comparing with multiplication4.OA.A.1RIT Range: 203-212Practice solving multiplication and division word problems. Some problems 4.OA.A.2 have remainders.Multiply 2- or 3-digit numbers by 1-digit numbers. No regrouping.4.NBT.B.5Multiply 3- or 4-digit numbers by 1-digit numbers. Regrouping (carrying) needed.4.NBT.B.5Multiply 2-digit numbers by 2-digit numbers. Regrouping (carrying) needed. 4.NBT.B.5Multiply a 1-digit number by a multi-digit number by decomposing the multi-digit number.4.NBT.B.545021547307500Use an area model to decompose factors and multiply.4.NBT.B.56+ | Operations and Algebraic Thinking | Expressions and Equations | RIT 203-212Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: 203-212Use an area model to decompose the larger factor and multiply.4.NBT.B.5RIT Range: 213-219Practice creating expressions with parentheses from real-world contexts.5.OA.A.2Solve multi-step expressions with parentheses. Place parentheses in an expression to make the expression equivalent to a given number.5.OA.A.1Solve and interpret fraction multiplication word problems.5.NF.B.6Practice evaluating powers of ten.5.NBT.A.2Practice changing expressions from words to math.5.OA.A.2Give the number of tens a number is being multiplied or divided by when the decimal is moved to the left or right.5.NBT.A.2RIT Range: 220-223Simplify algebraic expressions by combining like terms.6.EE.A.3Practice expanding expressions using the distributive property then combining like terms.6.EE.A.3Practice figuring out of a variable is dependent or independent.6.EE.C.9 Practice applying the distributive property to algebraic expressions.6.EE.A.3 Practice writing basic equations to model real-world situations.6.EE.B.6 | 6.EE.B.7Practice determining whether or not two algebraic expressions are equivalent by manipulating the expressions. These problems require you to combine like terms and apply the distributive property.Practice plugging in values to evaluate real-world algebraic expressions. These are introductory problems, so the expressions aren't too complicated.6.EE.A.36.EE.A.2Practice solving more challenging problems using the order of operations.6.EE.A.1Practice spotting the mistake in someone else's work as they attempt to solve one-step equations.6.EE.B.7 Create number line graphs of inequalities.6.EE.B.8Practice writing inequalities with variables to describe real-world situations. 6.EE.B.6 | 6.EE.B.8Practice solving equations in one step by multiplying or dividing a value from both sides.Practice solving equations in one step by adding or subtracting the same value from both sides.Practice solving equations in one step by adding or subtracting a number from both sides. These problems involve decimals and fractions.6.EE.B.7 | HSA-REI.B.36.EE.B.7 | HSA-REI.B.36.EE.B.76+ | Operations and Algebraic Thinking | Expressions and Equations | RIT 220-223Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: 220-223Practice solving equations in one step by multiplying or dividing a number from both sides. These problems involve decimals and fractions.Practice taking exponents of whole numbers. All exponents in these problems are either positive or zero.6.EE.B.76.EE.A.1Practice evaluating exponents that have fractional bases.6.EE.A.1Practice plugging in values to equations and checking to see if the equations hold true.Practice plugging in values to inequalities and checking to see if the inequalities hold true.Practice writing algebraic expressions to match verbal descriptions of mathematical operations.Practice writing slightly more complex algebraic expressions to model real- world situations.6.EE.B.56.EE.B.86.EE.A.26.EE.A.2Practice writing basic algebraic expressions to match verbal descriptions of 6.EE.A.2mathematical operations.Practice writing basic algebraic expressions to model real-world situations. 6.EE.A.2RIT Range: 224-227Simplify algebraic expressions by combining like terms. Coefficients on some terms are negative.Practice combining like terms using the distributive property. These problems involve adding and subtracting negative numbers.Practice solving word problems involving price discounts, taxes, and tip calculations.Practice figuring out which expressions are equivalent by applying your knowledge of negative numbers and the distributive property.Factor expressions like 3x-9 by applying the distributive property. (All expressions in this exercise are linear binomials.)7.EE.A.17.EE.A.17.EE.B.37.EE.A.17.EE.A.1Practice interpreting linear expressions7.EE.A.2Practice solving equations that take two steps to solve.7.EE.B.4 | HSA-REI.B.3Practice writing equations to model real-world situations, then solve the equations to answer interesting questions about the situations.Practice combining like terms for expressions that have rational coefficients. This requires adding and subtracting fractions.Practice solving word problems involving price markups and commission fees.7.EE.B.47.EE.A.17.EE.B.3Practice solving multi-step word problems. The numbers in these problems 7.EE.B.3may be fractions, decimals, and percents.6+ | Operations and Algebraic Thinking | Expressions and Equations | RIT 224-227Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: 224-227Practice solving equations that take two steps to solve. These problems involve arithmetic with fractions and decimals.7.EE.B.4RIT Range: 228-230Given two numbers in scientific notation, practice adding and subtracting them.8.EE.A.4Solve age word problems with a system of equations.8.EE.C.8Practice comparing two real-world quantities by approximating them with 8.EE.A.3powers of 10.A variety of questions about rates and proportional relationships involving graphs, tables, and equations.8.EE.B.5Given a linear equation with missing values, determine appropriate values 8.EE.C.7in order to have one, zero, or infinite solutions.Practice solving more challenging problems involving scientific notation.8.EE.A.4Determine the number of solutions of a given system of equations by considering its algebraic solution process.8.EE.C.8 | HSA-SSE.B.3Practice finding the cube root of a perfect cube positive integer.8.EE.A.2Practice solving equations by squaring or cubing both sides.8.EE.A.2Practice evaluating expressions by adding, subtracting, or multiplying exponents.Practice computing numbers raised to positive and negative exponents. Bases may be fractions.8.EE.A.18.EE.A.1Find the graph of a linear equation given in standard form.8.EE.C.7 | HSA-REI.D.10Determine the number of solutions of a given system of equations by considering its graph.Graph a system of equations in slope-intercept or standard form, and find their solution using the graphs.8.EE.C.8 | HSA-REI.D.10 | HSA-REI.D.118.EE.C.8 | HSA-REI.C.6 | HSA-REI.D.10 | HSA- REI.D.11Graphing proportional relationships8.EE.B.5Given the x or y value of a 2-variable equation solution, find the value for the other variable in the solution.Practice solving one-variable equations like 20 - 7x = 6x - 6, where the variable appears on both sides of the equals sign.8.EE.C.7 | HSA-REI.B.3 | HSA-REI.D.108.EE.C.7 | HSA-REI.B.3Practice solving problems using your knowledge of square and cube roots. 8.EE.A.2Practice expressing products and quotients in scientific notation.8.EE.A.4Practice solving equations with parentheses using the distributive property. 8.EE.C.7 | HSA-REI.B.3Solve linear equations that contain expressions with parentheses and the coefficients are rational numbers.8.EE.C.7 | HSA-REI.B.36+ | Operations and Algebraic Thinking | Expressions and Equations | RIT 228-230Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: 228-230Practice solving multiplication and division problems that involve powers of ten.8.EE.A.3Practice applying properties of exponents.8.EE.A.1Practice taking square roots of decimals and fractions.8.EE.A.2Practice expressing numbers in scientific notation.8.EE.A.4 Practice telling whether an equation has one, zero, or infinite solutions. 8.EE.C.7 Practice finding the square root of a perfect square positive integer.8.EE.A.2Solve systems of equations with any number of solutions using any solution method.Solve systems of equation with multi-step elimination (e.g., a manipulation is needed in order for x-values or y-values to cancel each other out).Solve systems of equation with one-step elimination (e.g., x-values or y- values cancel each other out).8.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.6 | HSA- SSE.B.38.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.6 | HSA- SSE.B.38.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.6Solve systems of equations where one of the equations is solved for one of 8.EE.C.8 | HSA-REI.C.6 | HSA-SSE.B.3the variables.Determine whether a couple of given systems of equations are equivalent or not to a third given system.Solve word problems by modeling them into a system of equations and solving it.Solve linear equations where the variable appears on both sides of the equation and the coefficients are decimals or fractions.8.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.58.EE.C.8 | HSA-APR.A.1 | HSA-CED.A.2 | HSA- CED.A.3 | HSA-REI.C.6 | HSA-SSE.B.38.EE.C.7 | HSA-REI.B.3Verify whether a given pair of values is a solution to a system of equations. 8.EE.C.8RIT Range: > 231Example: Add (2x?-3) and (7x?-4x+1).HSA-APR.A.1Example: Subtract (x?+2xy-y) and (3x+5xy+2y?).HSA-APR.A.1Example: Subtract -2x?+4x-1 from 6x?+3x-9.HSA-APR.A.1 Choose which step an error was made in adding or subtracting polynomials. HSA-APR.A.1 Example: Subtract a??+4a?b?-2b?? from -3a??+5a^2b?+2b??.HSA-APR.A.1Check whether an ordered pair is a solution of a system of two-variable linear inequalities.HSA-CED.A.3Given a two-variable linear inequality, check whether a given pair of values HSA-CED.A.3is a solution of the inequality.Given some information about a real-world context, analyze expressions containing unknown variables that model that context.HSA-SSE.A.1 | HSA-SSE.A.2Solve quadratic equations of the form x^2+bx+c by completing the square. HSA-REI.B.4 | HSA-SSE.B.36+ | Operations and Algebraic Thinking | Expressions and Equations | RIT > 231Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: > 231Solve quadratic equations of the form ax^2+bx+c by completing the square. HSA-REI.B.4 | HSA-SSE.B.3Practice the method of completing the square with quadratic expressions. HSA-REI.B.4Solve compound linear inequalities.HSA-REI.B.3Solve general word problems about real-world relationships that can be modeled by linear equations or functions.Determine the number of solutions of a given system of equations by considering its algebraic solution process.HSA-CED.A.2 | HSA-CED.A.48.EE.C.8 | HSA-SSE.B.3Convert linear equations between slope-intercept and standard forms.HSA-SSE.B.3Analyze quadratic equations in order to determine how many different real number solutions they have.Rewrite expressions of the form a(x)/b(x), where a is a polynomial b is a linear binomial, in the form q(x)+r(x)/b(x), where q and r are polynomials and the degree of r is less than the degree of b.Rewrite expressions of the form a(x)/b(x), where a is a polynomial b is a monomial, in the form q(x)+r(x)/b(x), where q and r are polynomials and the degree of r is less than the degree of b.Rewrite expressions of the form a(x)/b(x), where a and b are polynomials, in the form q(x)+r(x)/b(x), where q and r are polynomials and the degree of r is less than the degree of b.HSA-SSE.B.3HSA-APR.D.6HSA-APR.D.6HSA-APR.D.6Determine whether pairs of exponential expressions are equivalent.HSA-SSE.B.3Given some information about several unknown variables, evaluate an expression containing those variables.Given some information about several unknown variables, evaluate an expression containing those variables.Practice some problems that involve thinking about the conditions for obtaining extraneous solutions while solving radical equations.HSA-SSE.A.2 HSA-SSE.A.2 HSA-REI.A.2Factor quadratic expressions into the special products of the general forms HSA-SSE.A.2(x+a)^2, (x-a)^2, and (x+a)(x-a).Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b).HSA-SSE.A.2Factor "advanced" polynomials (i.e. polynomials of various degrees and or HSA-SSE.A.2 | HSA-SSE.B.3with two variables) using special product factorization methods.Factor quadratics of the form x?+bx+c.HSA-SSE.A.2 | HSA-SSE.B.3Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.HSA-SSE.A.2 | HSA-SSE.B.3Factor quadratics of the form ax?+bx+c.HSA-SSE.B.3Factor "advanced" polynomials (i.e. polynomials of various degrees and or HSA-SSE.A.2with two variables) using quadratic factorization methods.6+ | Operations and Algebraic Thinking | Expressions and Equations | RIT > 231Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: > 231Factor quadratic expressions of the general perfect square forms: (ax)^2+2abx+b^2 or (ax)^2-2abx+b^2. The factored expressions have the general forms (ax+b)^2 or (ax-b)^2.Find special products (perfect squares and difference of squares) of "advanced" binomials: binomials with leading coefficients other than 1; binomials with higher degrees; and binomials with two variables.Use the distributive property to express the product of a monomial and a polynomial as a single polynomial.HSA-SSE.A.2HSA-APR.A.1HSA-APR.A.1Express the product of two monomial expressions as a single monomialHSA-APR.A.1Use various methods in order to find all the zeros of polynomial expressions or functions.Understanding and solving problems with the formula for a finite geometric seriesEvaluate finite geometric series given in sigma notation, recursively, or explicitly.Draw the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.HSA-APR.B.3 | HSA-SSE.A.2 | HSA-SSE.B.3HSA-SSE.B.4 HSA-SSE.B.4 HSA-REI.D.10Find the graph of a linear equation given in standard form.8.EE.C.7 | HSA-REI.D.10Given the graph of a two-variable linear inequality, check whether a given pair of values is a solution of the inequality.Determine the number of solutions of a given system of equations by considering its graph.Find the range of values of one variable that corresponds to a given value of the other variable in a linear inequality.HSA-CED.A.38.EE.C.8 | HSA-REI.D.10 | HSA-REI.D.11HSA-CED.A.3Graph two-variable linear inequalities.HSA-CED.A.3 | HSA-REI.D.12Graph a system of equations in slope-intercept or standard form, and find their solution using the graphs.Find the range of values of one variable that corresponds to a given value of the other variable in a system of two-variable linear inequalities.Graph the line that represents a real-world relationship that is given verbally.Given the x or y value of a 2-variable equation solution, find the value for the other variable in the solution.8.EE.C.8 | HSA-REI.C.6 | HSA-REI.D.10 | HSA- REI.D.11HSA-CED.A.3HSA-REI.D.108.EE.C.7 | HSA-REI.B.3 | HSA-REI.D.10Fit an algebraic two-variable inequality to its appropriate graph.HSA-CED.A.3Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.HSA-SSE.B.3Find the intercepts of a line given a table of values.HSA-REI.D.106+ | Operations and Algebraic Thinking | Expressions and Equations | RIT > 231Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: > 231Solve word problems about real world relationships that are given in formulas.HSA-SSE.A.1Interpret the graphs of both linear and nonlinear functions.HSA-REI.D.10Solve word problems about real world relationships that are given in graphs.HSA-REI.D.10Given a function that models an exponential situation, rewrite the function HSA-SSE.A.1 | HSA-SSE.B.3in order to find its change for a different time unit.Given a function that models an exponential situation, rewrite the function HSA-SSE.A.1 | HSA-SSE.B.3in order to analyze its rate of change.Solve advanced and complicated equations using the power of graphs.HSA-REI.D.11Answer questions about real world situation, given the quadratic functions HSA-SSE.B.3that model them.Practice solving equations in one step by multiplying or dividing a value from both sides.6.EE.B.7 | HSA-REI.B.3Practice solving equations that take two steps to solve.7.EE.B.4 | HSA-REI.B.3Practice solving one-variable equations like 20 - 7x = 6x - 6, where the variable appears on both sides of the equals sign.Solve equations that have one rational expression whose numerator and denominator are linear expressions.8.EE.C.7 | HSA-REI.B.3HSA-REI.A.2Solve linear inequalities that take multiple steps to solve.HSA-REI.B.3Solve multi-variable formulas for a specific variable in order to solve some word problems.Find all the inputs that correspond to a given function output, using the function's graph.HSA-CED.A.4 HSA-REI.D.10Solve word problems that involve linear inequalities in two variables.HSA-CED.A.3 | HSA-SSE.A.1Solve word problems that involve systems of linear inequalities.HSA-CED.A.3 | HSA-SSE.A.1Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.Construct an equation or an inequality that model a given context. Modeling expressions can be quadratic, rational, or exponential.Use the distributive property to express the product of two binomials as a single polynomial.Find perfect squares of the forms (x+a)? and (x-a)?, and differences of squares of the form (x+a)(x-a).Use the distributive property to express the product of a binomial and a polynomial as a single polynomial.Example: Find the values of the variables to make the following equation true -11(y?-cy+2) = dy?+33y-f.HSA-SSE.B.3 HSA-CED.A.1 HSA-APR.A.1 HSA-APR.A.1 HSA-APR.A.1 HSA-APR.A.16+ | Operations and Algebraic Thinking | Expressions and Equations | RIT > 231Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: > 231More challenging multiplying monomial problems like find the area or find missing values to make an equation true.HSA-APR.A.1Practice solving equations with parentheses using the distributive property. 8.EE.C.7 | HSA-REI.B.3Solve linear equations that contain expressions with parentheses and the coefficients are rational numbers.Simplify rational expressions that contain rational expressions within their numerators or denominators.Practice solving equations in one step by adding or subtracting the same value from both sides.8.EE.C.7 | HSA-REI.B.3HSA-SSE.A.26.EE.B.7 | HSA-REI.B.3Practice solving inequalities in one step.HSA-REI.B.3Determine which ordered pairs are solutions to equations.HSA-REI.D.10Determine whether given polynomial identities are true, and whether given proofs of such identities are valid.Given a polynomial, determine the intervals in which it is positive or negative.HSA-APR.C.4HSA-APR.B.3Use the quadratic formula to find the roots of a quadratic function.HSA-REI.B.4Solve quadratic equations using the quadratic formula. some of the equations have real solutions while others have complex solutions.HSA-REI.B.4 | HSN-CN.C.7Solve advanced rational equations with multiple expressions.HSA-REI.A.2Use the PRT (Polynomial Remainder Theorem) to determine the factors of HSA-APR.B.2polynomials and their remainders when divided by linear expressions.Rewrite a given exponential expression in a specific desired form.HSA-SSE.B.3Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.Find the y-intercept, the zeroes ("roots"), and the vertex of the graphs of quadratic functions. Functions are given in standard, vertex, and factored form.Factor the numerator and the denominator of a rational expression and cancel out common monomial factors.Factor the numerator and the denominator of a rational expression and cancel out common binomial terms.Factor the numerator and the denominator of a rational expression using advanced methods, and cancel out common terms.HSA-SSE.B.3HSA-SSE.B.3HSA-APR.D.6 HSA-APR.D.6 HSA-APR.D.6Find the slope of a line on the coordinate plane.HSA-REI.D.10Find the slope of a line from its equation.HSA-REI.D.10Extract the slope of a line from its equationHSA-REI.D.10Find the slope of the line that goes through the two points that are given to you.HSA-REI.D.106+ | Operations and Algebraic Thinking | Expressions and Equations | RIT > 231Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: > 231Find the slope-intercept equation of a line from its graph.HSA-REI.D.10Find the equation of a line passing through two pointsHSA-REI.D.10Example: Solve 32^(x/3) = 8^(x-12).HSA-SSE.B.3Example: Solve 2^(3x+5) = 64^(x-7).HSA-SSE.B.3Solve square-root equations by first arranging them and then taking the square of both sides.HSA-REI.A.2Solve square-root equations by taking the square of both sides.HSA-REI.A.2Solve a linear equation where the coefficients are represented by letters.HSA-REI.B.3Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.HSA-REI.B.4 | HSA-SSE.B.3HSA-REI.B.4 | HSA-SSE.B.3Solve quadratic equations of the form (x+a)^2-b=0.HSA-REI.B.4Solve equations that have one rational expression whose numerator and denominator are polynomial expressions.Solve advanced equations by strategically using quadratic factorization methods.Rewrite an expression containing two unknown variables by using a given equation that contains those variables.Solve systems of equations with any number of solutions using any solution method.Solve systems of equation with multi-step elimination (e.g., a manipulation is needed in order for x-values or y-values to cancel each other out).Solve systems of equation with one-step elimination (e.g., x-values or y- values cancel each other out).HSA-REI.A.2HSA-REI.B.4 | HSA-SSE.B.3HSA-SSE.A.1 | HSA-SSE.A.28.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.6 | HSA- SSE.B.38.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.6 | HSA- SSE.B.38.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.6Solve systems of equations where one of the equations is solved for one of 8.EE.C.8 | HSA-REI.C.6 | HSA-SSE.B.3the variables.Practice the connection between the graphical representation of equations HSA-REI.D.11and their algebraic solutions.Determine whether a couple of given systems of equations are equivalent or not to a third given system.Solve word problems by modeling them into a system of equations and solving it.Analyze the process of solving a quadratic equation by taking the square root.Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.8.EE.C.8 | HSA-APR.A.1 | HSA-REI.C.58.EE.C.8 | HSA-APR.A.1 | HSA-CED.A.2 | HSA- CED.A.3 | HSA-REI.C.6 | HSA-SSE.B.3HSA-REI.A.1 | HSA-REI.B.4HSA-APR.B.3 | HSA-SSE.A.2 | HSA-SSE.B.36+ | Operations and Algebraic Thinking | Expressions and Equations | RIT > 231Operations and Algebraic ThinkingExpressions and EquationsStandards AlignmentRIT Range: > 231Solve linear equations where the variable appears on both sides of the equation and the coefficients are decimals or fractions.Practice writing finite geometric series like 3 + 6 + 12 + 24 in sigma notation.You've had practice with a few different forms of linear equations. Now use your skills.Operations and Algebraic ThinkingUse Functions to Model Relationships8.EE.C.7 | HSA-REI.B.3HSA-SSE.B.4 HSA-REI.D.10Standards AlignmentRIT Range: 203-212Generate terms in a pattern when given a rule. Identify features of a pattern that are not explicit to the rule itself.4.OA.C.5RIT Range: 213-219Find the distance between points, graph points, and interpret data on coordinate planes to solve word problems.5.G.A.2Plot a given point on the coordinate plane.5.G.A.2Generate patterns using given rules. Identify relationships between terms. 5.OA.B.3Graph ordered pairs consisting of corresponding terms from the patterns.RIT Range: 228-230Compare features of two linear functions represented in different ways.8.F.A.2 | HSF-IF.C.9Compare features of two real-world relationships that can be modeled by linear functions, where the functions are represented in different ways.8.F.A.2 | HSF-IF.C.9 | HSF-LE.B.5Find a linear function that represents a real-world relationship that is given 8.F.B.4 | HSF-BF.A.1 | HSF-LE.A.2 | HSF-LE.B.5verbally.Given the graph of a function, determine its domain or range.8.F.A.1 | HSF-IF.A.1 | HSF-IF.B.5Determine the domain of a function according to the algebraic limitations of that function.Interpret expressions with function notation in terms of the context that the function models.8.F.A.1 | HSF-IF.A.1 | HSF-IF.B.58.F.A.1 | HSF-IF.A.1 | HSF-IF.A.2Evaluate functions for specific inputs given the formula of the function.8.F.A.1 | HSF-IF.A.1 | HSF-IF.A.2Evaluate expressions that contain function notation, given the functions' graphs.Find all the inputs that correspond to a given function output, using the function's formula.8.F.A.1 | HSF-IF.A.1 | HSF-IF.A.28.F.A.1 | HSF-IF.A.1 | HSF-IF.A.26+ | Operations and Algebraic Thinking | Use Functions to Model Relationships | RIT 228-230Operations and Algebraic ThinkingUse Functions to Model RelationshipsStandards AlignmentRIT Range: 228-230Create functions that match one variable to the other in a two-variable equation.8.F.A.1 | HSF-IF.A.1 | HSF-IF.A.2 | HSF-LE.A.2Draw the graph of a line given in slope-intercept form. For example, graph 8.F.A.1 | 8.F.A.3 | HSF-IF.C.7y = 3x + 2.Find the graph of a linear equation given in standard form.8.F.A.1 | HSF-IF.C.7Given the x or y value of a 2-variable equation solution, find the value for the other variable in the solution.8.F.A.1 | HSF-IF.C.7Determine which ordered pair represents a solution to a graph or equation. 8.F.B.4Highlight intervals on the domain of a function where it's only increasing or 8.F.B.5 | HSF-IF.B.4 | HSF-IF.C.7only decreasing.Find the intercepts of a line given a table of values.8.F.A.1Match features of graphs of modeling functions to their real-world meaning.Use information about a situation to figure out the domain of the function which models it.Solve word problems about real world relationships that are given in formulas.8.F.B.5 | HSF-IF.B.4 | HSF-IF.C.78.F.A.1 | HSF-IF.A.1 | HSF-IF.B.58.F.A.3 | 8.F.B.4 | HSF-LE.B.5Interpret the graphs of both linear and nonlinear functions.8.F.B.5 Look at the graph of an equation to find x-intercepts and y-intercepts8.F.A.1 Determine if a relationship is linear or nonlinear.8.F.A.3Determine which ordered pairs are solutions to equations.8.F.A.1Highlight intervals on the domain of a function where it's entirely positive or entirely negative.8.F.B.5 | HSF-IF.B.4 | HSF-IF.C.7Determine whether a given graph represents a function.8.F.A.1 | HSF-IF.A.1Given the graph of a function, find all of its relative maximum and minimum points.Determine whether a table of values of a relationship represents a function.8.F.B.5 | HSF-IF.B.4 | HSF-IF.C.7| HSF-IF.A.1Find the slope of a line on the coordinate plane.8.F.B.4 | HSF-LE.A.2Find the slope of a line from its equation.8.F.B.4Extract the slope of a line from its equation8.F.B.4Find the slope of the line that goes through the two points that are given to you.8.F.B.4 | HSF-LE.A.2Find the slope-intercept equation of a line from its graph.8.F.A.1 | 8.F.A.3 | 8.F.B.4 | HSF-LE.A.2Find the equation of a line passing through two points8.F.A.1 | 8.F.A.3 | 8.F.B.4 | HSF-LE.A.26+ | Operations and Algebraic Thinking | Use Functions to Model Relationships | RIT 228-230Operations and Algebraic ThinkingUse Functions to Model RelationshipsStandards AlignmentRIT Range: 228-230Solve linear equations for the x-intercept and y-intercept8.F.A.3 | HSF-IF.C.7DEPRECATED Solving for the y-intercept8.F.B.4You've had practice with a few different forms of linear equations. Now use your skills.8.F.A.1 | 8.F.A.3 | 8.F.B.4 | HSF-LE.A.2RIT Range: > 231Given the formula of a rational function, determine how it behaves around HSF-IF.C.7its vertical asymptote.Find and represent the average rate of change of a real-world relationship. HSF-IF.B.6Find the average rate of change of a function over a given interval.HSF-IF.B.6Given the sine (or cosine) of an angle, find its cosine (or sine) using the Pythagorean pare the properties of two quadratic functions, each represented in a different way.HSF-TF.C.8 HSF-IF.C.9Compare features of two linear functions represented in different ways.8.F.A.2 | HSF-IF.C.9Compare features of two real-world relationships that can be modeled by linear functions, where the functions are represented in different pare various features between two functions, each represented in a different way.Practice analyzing the end behavior of two functions that model similar real-world relationship, where one function is exponential and the other is polynomial.| HSF-IF.C.9 | HSF-LE.B.5HSF-IF.C.9HSF-LE.A.3Given the formulas of two functions, find the formula of their composition. HSF-BF.A.1Construct exponential functions of the basic form f(x)=a*r^x given the initial value of the function and the ratio by which it increases for each unit. Construct exponential functions of the basic form f(x)=a*r^x, either when given a table with two input-output pairs, or when given the graph of the function.Given a verbal description of the rate of change of a real world situation, find the exponential function that models it.Solve general word problems about real-world relationships that can be modeled by linear equations or functions.Find a linear function that represents a real-world relationship that is given verbally.HSF-BF.A.1 | HSF-LE.A.2HSF-BF.A.1 | HSF-LE.A.2HSF-BF.A.1 | HSF-IF.C.8 | HSF-LE.A.1 | HSF- LE.A.2 | HSF-LE.B.5HSF-BF.A.1 | HSF-LE.A.2 | HSF-LE.B.58.F.B.4 | HSF-BF.A.1 | HSF-LE.A.2 | HSF-LE.B.5Given a few features of a sinusoidal function, find its formula.HSF-BF.B.3 | HSF-TF.B.5Write equations in point-slope form given two pairs of values, and convert HSF-LE.A.2 | HSF-LE.B.5the equation into slope-intercept form.Convert linear equations between slope-intercept and standard forms.HSF-IF.C.86+ | Operations and Algebraic Thinking | Use Functions to Model Relationships | RIT > 231Operations and Algebraic ThinkingUse Functions to Model RelationshipsStandards AlignmentRIT Range: > 231Given the formula of a polynomial function, determine whether that function is even, odd, or neither.Determine the domain of piecewise functions whose assignment rules have different expression types.Analyze polynomial functions to determine how they behave as the input variable increases to positive infinity or decreases to negative infinity.Given a table with values of two quantities over time, determine whether the quantities form grow linearly or exponentially.HSF-BF.B.3 HSF-IF.A.1 HSF-IF.C.7HSF-BF.A.1 | HSF-LE.A.1Given the graph of a function, determine its domain or range.8.F.A.1 | HSF-IF.A.1 | HSF-IF.B.5Determine the domain of functions whose expressions are a combination of different types of assignment rules.HSF-IF.A.1Find the domain and range of a piecewise function given its formula.HSF-IF.A.1 | HSF-IF.B.5Determine the domain of a function according to the algebraic limitations of that function. Given a rati o nal functi o n, deter m ine ho w it be have s as x a pproaches + ?? o r -??. 8.F.A.1 | HSF-IF.A.1 | HSF-IF.B.5HSF-IF.C.7Determine whether pairs of exponential expressions are equivalent.HSF-IF.C.8Given the formulas of two functions, evaluate the composition of the two functions at a given input.Given the graphs, or some tables of values, of two functions, evaluate the composition of those functions at a given input.HSF-BF.A.1HSF-BF.A.1Evaluate functions for specific inputs given the graph of the function.HSF-IF.A.1 | HSF-IF.A.2Evaluate any logarithm in a calculator with the use of the change of base fo rmula. Example: Evaluate log?…(100). Given the graph of a step function, find the function's outputs for given specific inputs.HSF-LE.A.4HSF-IF.A.1 | HSF-IF.A.2Given the formula of a piecewise function, evaluate it for a specific input. HSF-IF.A.1 | HSF-IF.A.2 Find the first few terms of sequences that are defined recursively.HSF-IF.A.1 | HSF-IF.A.2 Given the graph of a function, determine if it's even, odd, or neither.HSF-BF.B.3Given the explicit formula of an arithmetic sequence, find its recursive formula, and vice versa.Given the explicit formula of a geometric sequence, find its recursive formula, and vice versa.HSF-BF.A.2 | HSF-IF.A.1HSF-BF.A.2 | HSF-IF.A.1Solve problems such as: The first four terms in an arithmetic sequence are HSF-BF.A.2 | HSF-IF.A.112, 5, -2, and -9. Find an explicit formula for the sequence.Solve word problems about exponential situations.HSF-LE.A.4Given the formula of a sinusoidal function, determine its amplitude.HSF-IF.C.7 | HSF-TF.B.56+ | Operations and Algebraic Thinking | Use Functions to Model Relationships | RIT > 231Operations and Algebraic ThinkingUse Functions to Model RelationshipsStandards AlignmentRIT Range: > 231Given the formula of a sinusoidal function, determine its midline equation. HSF-IF.C.7 | HSF-TF.B.5Given the formula of a sinusoidal function, determine its period.HSF-IF.C.7 | HSF-TF.B.5Interpret expressions with function notation in terms of the context that the function models.8.F.A.1 | HSF-IF.A.1 | HSF-IF.A.2Evaluate functions for specific inputs given the formula of the function.8.F.A.1 | HSF-IF.A.1 | HSF-IF.A.2Evaluate expressions that contain function notation, given the functions' graphs.Find all the inputs that correspond to a given function output, using the function's formula.Create functions that match one variable to the other in a two-variable equation.8.F.A.1 | HSF-IF.A.1 | HSF-IF.A.28.F.A.1 | HSF-IF.A.1 | HSF-IF.A.28.F.A.1 | HSF-IF.A.1 | HSF-IF.A.2 | HSF-LE.A.2Evaluating geometric sequences 1HSF-IF.A.3Evaluating geometric sequences 2HSF-IF.A.3Draw the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.8.F.A.1 | 8.F.A.3 | HSF-IF.C.7Find the graph of a linear equation given in standard form.8.F.A.1 | HSF-IF.C.7Graph quadratic functions given in the standard form ax^2+bx+c.HSF-IF.C.7 Graph quadratic functions that are given in the vertex form a(x+b)^2+c. HSF-IF.C.7 Graph quadratic functions given in any form.HSF-IF.C.7Graph the line that represents a real-world relationship that is given verbally.HSF-IF.C.7Given the graph of a nonlinear piecewise function, find its formula.HSF-IF.C.7Given the x or y value of a 2-variable equation solution, find the value for the other variable in the solution.8.F.A.1 | HSF-IF.C.7Graph quadratic functions that are given in factored form.HSF-IF.C.7Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.HSF-IF.C.7Graph functions that contain absolute value expressions, like f(x)=|x+3|+2. HSF-IF.C.7Graph exponential functions of the basic form f(x)=a*r^x while considering HSF-IF.C.7the end behavior of the function.Graph exponential functions and find the appropriate graph given the function.Graph logarithmic functions and find the appropriate graph given the function.Given the formula of a square-root or a cube-root function, find the appropriate graph.HSF-IF.C.7 HSF-IF.C.7 HSF-IF.C.76+ | Operations and Algebraic Thinking | Use Functions to Model Relationships | RIT > 231Operations and Algebraic ThinkingUse Functions to Model RelationshipsStandards AlignmentRIT Range: > 231Determine which of four graphs fits the formula of a given function.HSF-IF.C.7Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.HSF-IF.C.8Highlight intervals on the domain of a function where it's only increasing or 8.F.B.5 | HSF-IF.B.4 | HSF-IF.C.7only decreasing.Match features of graphs of modeling functions to their real-world meaning.8.F.B.5 | HSF-IF.B.4 | HSF-IF.C.7Use information about a situation to figure out the domain of the function 8.F.A.1 | HSF-IF.A.1 | HSF-IF.B.5which models it.Solve word problems about real world relationships that are given in formulas.Solve word problems about real world relationships that are given in graphs.8.F.A.3 | 8.F.B.4 | HSF-LE.B.5HSF-IF.C.7 | HSF-LE.B.5Solve word problems about real world relationships that are given in tables. HSF-IF.B.4 | HSF-LE.A.2 | HSF-LE.B.5Given a function that models an exponential situation, rewrite the function HSF-IF.C.8 | HSF-LE.A.1 | HSF-LE.B.5in order to find its change for a different time unit.Given a function that models an exponential situation, rewrite the function HSF-IF.C.8 | HSF-LE.A.1 | HSF-LE.B.5in order to analyze its rate of change.Given the graph that models a real world context, answer a question about HSF-IF.B.4 the periodicity of the graph.Inverses of linear functionsHSF-BF.B.4aAnswer questions about real world situation, given the quadratic functions HSF-IF.C.8that model them.Find all the inputs that correspond to a given function output, using the function's graph.Given two basic functions that model a real-world situation, compose them in order to model a more complex situation.Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.Given the description of a real-world relationship, find the sinusoidal function that models it.Given the description of a real-world relationship, find the sinusoidal function that models it. The functions in this exercise have a phase (horizontal) shift.HSF-IF.A.1 | HSF-IF.A.2HSF-BF.A.1HSF-IF.C.8 | HSF-LE.A.1 | HSF-LE.B.5HSF-TF.B.5 HSF-TF.B.5Given the graph of a sinusoidal function, determine its period.HSF-IF.C.7 | HSF-TF.B.5Draw the graph of a piecewise function or determine its formula from its graph.Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities.HSF-IF.A.1 | HSF-IF.C.7HSF-IF.C.76+ | Operations and Algebraic Thinking | Use Functions to Model Relationships | RIT > 231Operations and Algebraic ThinkingUse Functions to Model RelationshipsStandards AlignmentRIT Range: > 231Highlight intervals on the domain of a function where it's entirely positive or entirely negative.Given a polynomial, determine the intervals in which it is positive or negative.8.F.B.5 | HSF-IF.B.4 | HSF-IF.C.7HSF-IF.C.7Given the equation of a quadratic function, determine its range.HSF-IF.A.1Given the graph that models a real world context, answer a question about HSF-IF.B.4 the end behavior of the graph.Determine whether a given graph represents a function.8.F.A.1 | HSF-IF.A.1Given the graph of a function, find its absolute maximum and minimum points.Given the graph of a function, find all of its relative maximum and minimum points.Determine whether a table of values of a relationship represents a function.Given a verbal description of a real-world relationship, determine the sequence that models that relationship.Find the recursive formula of an arithmetic sequence given the first few terms or given an explicit formula.Find the recursive formula of a geometric sequence given the first few terms or given an explicit formula.HSF-IF.B.4 | HSF-IF.C.78.F.B.5 | HSF-IF.B.4 | HSF-IF.C.78.F.A.1 | HSF-IF.A.1HSF-BF.A.1 | HSF-BF.A.2 | HSF-LE.A.1HSF-BF.A.2 | HSF-IF.A.1 HSF-BF.A.2 | HSF-IF.A.1Rewrite a given exponential expression in a specific desired form.HSF-IF.C.8Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.Find the y-intercept, the zeroes ("roots"), and the vertex of the graphs of quadratic functions. Functions are given in standard, vertex, and factored form.Solve problems such as: The first four terms in a geometric sequence are 1/3, 1, 3, and 9. Find an explicit formula for the sequence.Shift functions horizontally and vertically, and practice the relationship between the graphical and the algebraic representations of those shifts. Given the graphs of functions f and g where g is a transformation of f, determine the formula of g in terms of f.HSF-IF.C.8 | HSF-LE.A.1 | HSF-LE.B.5HSF-IF.C.8HSF-BF.A.2 | HSF-IF.A.1HSF-BF.B.3HSF-BF.B.3Find the slope of a line on the coordinate plane.8.F.B.4 | HSF-LE.A.2Find the slope of the line that goes through the two points that are given to you.8.F.B.4 | HSF-LE.A.2Find the slope-intercept equation of a line from its graph.8.F.A.1 | 8.F.A.3 | 8.F.B.4 | HSF-LE.A.2Find the equation of a line passing through two points8.F.A.1 | 8.F.A.3 | 8.F.B.4 | HSF-LE.A.2Solve exponential equations that have 2 or other numbers at the base of the exponential term.HSF-LE.A.46+ | Operations and Algebraic Thinking | Use Functions to Model Relationships | RIT > 231Operations and Algebraic ThinkingUse Functions to Model RelationshipsStandards AlignmentRIT Range: > 231Solve linear equations for the x-intercept and y-intercept8.F.A.3 | HSF-IF.C.7Given a verbal description of a real-world relationship, determine whether HSF-LE.A.1that relationship is linear or exponential.Solve exponential equations that have 10 or e at the base of the exponential term.Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.You've had practice with a few different forms of linear equations. Now use your skills.Statistics and ProbabilityInterpreting Categorical and Quantitative DataHSF-LE.A.4HSF-IF.C.7 | HSF-IF.C.88.F.A.1 | 8.F.A.3 | 8.F.B.4 | HSF-LE.A.2Standards AlignmentRIT Range: 161-178Read and interpret bar graphs.1.MD.C.4RIT Range: 179-191Practice creating line plots (dot plots) from data sets.2.MD.D.9Practice creating bar graphs (bar charts) from data sets.2.MD.D.9 Use bar graphs to solve addition and subtraction word problems.2.MD.D.10 Answer questions using line plots and data sets.2.MD.D.9Read and interpret picture graphs.2.MD.D.10RIT Range: 192 - 203Creating line plots3.MD.B.4RIT Range: 192-202Create a bar graph with the data given.3.MD.B.3Create and interpret picture graphs.3.MD.B.3Read and interpret a double bar graphs.3.MD.B.3 Interpret picture graphs to answer questions about a context.3.MD.B.3 Interpret bar graphs to answer questions about a context.3.MD.B.3Use picture graphs to solve word problems.3.MD.B.36+ | Statistics and Probability | Interpreting Categorical and Quantitative Data | RIT 203-212Statistics and ProbabilityInterpreting Categorical and Quantitative DataStandards AlignmentRIT Range: 203-212Create and interpret dot plots using data with fractions. Fraction operations include addition and subtraction.4.MD.B.4RIT Range: 213-219Interpret fraction data on dot plots to solve word problems.5.MD.B.2RIT Range: 220-223Practice reading information presented in box plots.6.SP.A.2 | 6.SP.A.3 | 6.SP.B.4 | 6.SP.B.5Practice reading basic dot plots and frequency tables.6.SP.B.4More practice making box plots to summarize data sets.6.SP.B.4Practice computing the mean of data sets presented in a variety of formats, such as frequency tables and dot plots.6.SP.B.4Practice some nifty new vocab for describing data distributions.6.SP.A.2Practice interpreting and comparing dot plots, histograms, and box plots.6.SP.B.4Practice creating dot plots. Dot plots are very similar to frequency tables, but they make it easier to see the data.6.SP.B.4Practice creating frequency tables from small data sets.6.SP.B.4Practice creating histograms.6.SP.B.4Practice figuring out how the mean and median are affected when a data point is added to, taken from, or shifted within a data set.6.SP.A.3Practice understanding the meaning of quartiles of data sets.6.SP.B.4Practice reading histograms.6.SP.B.4Practice explaining the shapes of data distributions. Some distributions are 6.SP.A.2symmetrical, perfectly balanced on the left and right. Other distributions are unbalanced. We say they are €?skewed€?and have €?tails." Practice spotting the difference between statistical and non-statistical questions.6.SP.A.1RIT Range: 224-227Practice comparing distributions that are presented in dot plots, histograms, and box plots.SP.B.3 | 7.SP.B.4RIT Range: 228-230Practice plotting points to construct a scatter plot.8.SP.A.1Practice estimating the equation of a line of best fit through data points in a scatter plot. Then, use the equation to make a prediction.8.SP.A.36+ | Statistics and Probability | Interpreting Categorical and Quantitative Data | RIT 228-230Statistics and ProbabilityInterpreting Categorical and Quantitative DataStandards AlignmentRIT Range: 228-230Do you understand how two-way tables really work? Here's your chance to 8.SP.A.4 practice. Go get 'em! You got this!Practice making sense of trends in scatter plots. That is, explain what trends mean in terms of real-world quantities.Given a scatter plot, can you estimate the slope of the line of best fit that goes through the data points?A good scatter plot has the independent variable on the x-axis and the dependent variable on the y-axis. Also, the scale of both axes should be reasonable, making the data as easy to read as possible. In these practice problems, we practice telling good s8.SP.A.1SP.A.3 | HSS-ID.B.6 | HSS-ID.C.78.SP.A.1Given a random assortment of points, draw a line of best fit through them. 8.SP.A.2 | HSS-ID.B.6Practice identifying the types of correlations shown in scatter plots. Sometimes we see linear correlations (positive or negative), sometimes we see non-linear correlations (the data seems to follow a curve), and other times we don't see any correlation aPractice interpreting two-way frequency tables. For example, what does the cell in the top left tell you?8.SP.A.18.SP.A.4Practice interpreting two-way relative frequency tables8.SP.A.4Given a Venn diagram or information about a relationship, create a two- way frequency table.Practice creating two-way relative frequency tables from a two-way frequency table.8.SP.A.48.SP.A.4RIT Range: > 231Match correlation coefficients to scatterplots to build a deeper intuition behind correlation coefficients.HSS-ID.C.8Practice applying the 68-95-99.7 empirical rule.HSS-ID.A.4Determine if a quadratic or exponential model fits a data set better, then use the model to make a prediction.HSS-ID.B.6Take a look at two different data distributions and draw some comparisons. HSS-ID.A.1 | HSS-ID.A.2 | HSS-ID.A.3Given a scatter plot, can you estimate the slope of the line of best fit that goes through the data points?8.SP.A.3 | HSS-ID.B.6 | HSS-ID.C.7Given a random assortment of points, draw a line of best fit through them. 8.SP.A.2 | HSS-ID.B.6Calculate the standard deviation of a population.HSS-ID.A.2Analyze categorical data to find some trends.HSS-ID.B.545021579438500Determines if a statistical study is a sample study, an experiment, or an observational study.HSS-ID.C.96+ | Statistics and Probability | Interpreting Categorical and Quantitative Data | RIT > 231Statistics and ProbabilityInterpreting Categorical and Quantitative DataStandards AlignmentRIT Range: > 231Find the z-score of a particular measurement given the mean and standard deviation.HSS-ID.A.4Use a z-table to find the probability of a particular measurement.HSS-ID.A.4Use a z-table to find the probability that a particular measurement is in a range.Statistics and ProbabilityUsing Sampling and Probability to Make DecisionsHSS-ID.A.4Standards AlignmentRIT Range: 224-227Practice using sample space diagrams to find probabilities.7.SP.C.8Practice making reasonable estimates of the likelihood of future events based on past experience.Practice counting possible outcomes in a variety of situations. These problems cover everything from counting the number of ways to get dressed in the morning to counting the number of ways to build a custom pizza.7.SP.C.67.SP.C.8Given a random sample, practice figuring out what can we reasonably infer 7.SP.A.1about the entire population?Practice finding probabilities of events, such as rolling dice, drawing marbles out of a bag, and spinning spinners.Practice creating probability models and understand what makes a valid probability model.7.SP.C.77.SP.C.7Practice checking if sample space diagrams match a compound event.7.SP.C.8Practice expressing probabilities in different forms (fractions, decimals, and percents).7.SP.C.5Practice predicting the number of times a certain event will happen.7.SP.C.7Practice figuring out whether we took a random sample and whether we're able to draw valid conclusions from our data.7.SP.A.1 | HSS-IC.A.1RIT Range: > 231Find four probabilities for each problem: P(A), P(B), P(A and B), and P(A or B).HSS-CP.B.7The union, complement, and intersection of sets.HSS-CP.A.1Find dependent probabilities like P(A | B) or P(B | A) for a variety of contexts.HSS-CP.B.6Answer interesting questions about subsets of sample spaces.HSS-CP.A.16+ | Statistics and Probability | Using Sampling and Probability to Make Decisions | RIT > 231Statistics and ProbabilityUsing Sampling and Probability to Make DecisionsStandards AlignmentRIT Range: > 231Look at the results of different experiments, and determine if they are statistically significant.Show that you have mastery over the idea behind hypothesis testing by calculating some probabilities and drawing conclusions.HSS-IC.B.5HSS-IC.A.2Determine if two events are dependent or independent.HSS-CP.A.2 | HSS-CP.A.3Analyze categorical data to find some trends.HSS-CP.A.4 | HSS-CP.A.5 | HSS-CP.B.6Determines if a statistical study is a sample study, an experiment, or an observational study.Practice figuring out whether we took a random sample and whether we're able to draw valid conclusions from our data.The Real and Complex Number SystemsExtend and Use PropertiesHSS-IC.B.3 | HSS-IC.B.6 7.SP.A.1 | HSS-IC.A.1Standards AlignmentRIT Range: < 160Practice counting which group has more objects..C.6RIT Range: 161-178Comparing two-digit numbers1.NBT.B.3RIT Range: 161-178Practice grouping objects by tens.1.NBT.B.2Practice dividing shapes into 2 or 4 equal sections.1.G.A.3Practice breaking numbers apart into tens and ones.1.NBT.B.2RIT Range: 179-191Practice more challenging problems comparing numbers within 1000.2.NBT.A.4 Practice telling if shapes are divided into 2 or 4 equal sections.2.G.A.3 Practice thinking about 3-digit numbers as hundreds, tens, and ones.2.NBT.A.1 Practice breaking numbers into hundreds, tens, and ones.2.NBT.A.3RIT Range: 192 - 203Fractions on the number line 13.NF.A.26+ | The Real and Complex Number Systems | Extend and Use Properties | RIT 192-202The Real and Complex Number SystemsExtend and Use PropertiesStandards AlignmentRIT Range: 192-202Unit fractions on the number line3.NF.A.2a | 3.NF.A.2bRIT Range: 192-202Compare two fractions that have either the same numerator or denominator. Compare two fractions that have the same denominator using greater and less than pare two fractions that have the same numerator using greater and less than symbols.3.NF.A.33.NF.A.33.NF.A.3Practice comparing fractions with the help of visuals aides.3.NF.A.3Identify unit fractions when given a visual or a context.3.G.A.2 | 3.NF.A.1Graph and identify equivalent fractions on a number line.3.NF.A.3 Identify and create equivalent fractions using visual models.3.NF.A.3 Identify the fraction of a whole that is shaded.3.NF.A.1 Practice making groups of 10 and 100 while adding 3-digit numbers.3.NBT.A.2 Practice identifying numerators and denominators in fractions.3.NF.A.1 Identify the fraction of a whole that is shaded.3.NF.A.1 Practice telling if a shape has been divided into equal parts.3.G.A.2 | 3.NF.A.1RIT Range: 203-212Comparing decimals and fractions4.NF.C.7Comparing decimals visually4.NF.C.7Decompose fractions with denominators of 1004.NF.C.5Equivalent fractions with denominators of 10 and 1004.NF.C.5Equivalent fractions with denominators of 10 and 100 intuition4.NF.C.5RIT Range: 204 - 212Comparing decimals 14.NF.C.7Composite numbers4.OA.B.4Fractions as division by 10 or 1004.NF.C.6Decimals on the number line 14.NF.C.6Decimals on the number line 24.NF.C.66+ | The Real and Complex Number Systems | Extend and Use Properties | RIT 204 - 212The Real and Complex Number SystemsExtend and Use PropertiesStandards AlignmentRIT Range: 204 - 212Prime numbers4.OA.B.4RIT Range: 203-212Practice rewriting fractions to have the same denominator.4.NF.A.2Practice comparing two fractions with different denominators with greater and less than symbols. Practice comparing fractions and mixed numbers that have unlike denominators.4.NF.A.24.NF.A.2Use your place value skills to practice comparing whole numbers.4.NBT.A.2Compare multi-digit numbers that challenge your place value understanding4.NBT.A.2Sal arranges digits to make the largest or smallest possible number.4.NBT.A.1Practice using the same whole to find equivalent fractions.4.NF.A.2Practice dividing whole numbers by 10.4.NBT.A.1Practice making equivalent fractions by multiplying the numerator and denominator by the same number.4.NF.A.1Practice multiplying and dividing whole numbers by ten.4.NBT.A.1Practice multiplying whole numbers by 10.4.NBT.A.1Practice reading and writing numbers written in expanded form. Example: The expanded form of 376 is 300 + 70 + 6.Practice working with whole numbers in written form. For example, "one thousand four hundred three" is the written form of 1403.4.NBT.A.24.NBT.A.2Practice ordering 3 fractions from least to greatest.4.NF.A.2Practice thinking about the value of each digit in a number.4.NBT.A.2Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.Practice problems to challenge your understanding of whole number place value4.NBT.A.14.NBT.A.2Practice finding equivalent fractions. These problems show you pictures of 4.NF.A.1fractions to help you out.Practice comparing fractions by looking at pictures. Fractions in these problems do not have common denominators.4.NF.A.2RIT Range: 213-219Compare 2 numbers to thousandths based on meanings of the digits in each place.5.NBT.A.16+ | The Real and Complex Number Systems | Extend and Use Properties | RIT 213-219The Real and Complex Number SystemsExtend and Use PropertiesStandards AlignmentRIT Range: 213-219Graph and find the distance between point in first quadrant of coordinate plane.5.G.A.1Plot a given point on the coordinate plane.5.G.A.1Practice identifying place value names for decimal numbers. For example, the 3 in 4.563 is in the thousandths place.5.NBT.A.3Identify points in the first quadrant of a coordinate plane.5.G.A.1Practice evaluating powers of ten.5.NBT.A.2Give the number of tens a number is being multiplied or divided by when the decimal is moved to the left or right.5.NBT.A.2Practice understanding that the fraction bar really means division.5.NF.B.3Practice word problems that involve using the fraction bar as division.5.NF.B.3Practice identifying the value of one of the digits in a decimal number. For example, the 3 in 4.563 has a value of 0.003.5.NBT.A.1RIT Range: 220-223Practice finding the absolute value of a number, like -4 or 3.6.NS.C.7Practice understanding the meaning of absolute value in real-world scenarios.6.NS.C.7Write an inequality to compare absolute values.6.NS.C.7Practice more challenging comparison problems with absolute value.6.NS.C.7Practice solving word problems by interpreting the meaning of points plotted on an xy coordinate system.6.NS.C.6 | 6.NS.C.8Practice placing positive and negative decimal numbers on the number line. 6.NS.C.6Practice placing positive and negative fractions and decimals on the number line.6.NS.C.6Practice graphing points and identifying which quadrants they're in.6.NS.C.6Practice plotting points like (-2, 4).6.NS.C.6Practice explaining the meaning of negative numbers in different scenarios. 6.NS.C.5Identify positive and negative integers on the number line.6.NS.C.6Practice more challenging problems where you identify positive and negative integers on a number line that doesn't have zero labeled. Practice finding the opposites of numbers. Numbers are opposites when they're on opposite sides of the number line the same distance from zero. Practice solving more challenging problems finding the opposites of numbers. Numbers are opposites when they're on opposite sides of the number line the same distance from zero.6.NS.C.66.NS.C.66.NS.C.66+ | The Real and Complex Number Systems | Extend and Use Properties | RIT 220-223The Real and Complex Number SystemsExtend and Use PropertiesStandards AlignmentRIT Range: 220-223Practice putting positive and negative numbers in order. For example, -28, 6.NS.C.712, -51, and 43.Practice putting positive and negative fractions and decimals in order. For example, -12/4, -2.5, and 3.25.6.NS.C.7Practice reflecting points across axes on the xy coordinate plane.6.NS.C.6 | 6.NS.C.8Practice finding the distance between two points on the coordinate plane that share the same x- or y-coordinate.Practice comparing positive and negative numbers by thinking about their positions on the number line. Numbers to the right are greater than numbers to the left.6.NS.C.6 | 6.NS.C.86.NS.C.7Practice writing inequalities to describe real-world situations.6.NS.C.7RIT Range: 228-230Practice using a calculator to find the approximate decimal values of irrational numbers.8.NS.A.2Practice comparing irrational numbers without using a calculator.8.NS.A.2Practice finding the approximate value of square roots by thinking about perfect squares.8.NS.A.2Practice converting 1- and 2-digit repeating decimals to fractions.8.NS.A.1 Practice converting multi-digit repeating decimals to fractions.8.NS.A.1 Practice identifying whether numbers are rational or irrational.8.NS.A.1Practice finding the approximate value of square roots by thinking about perfect squares.Practice writing fractions as repeating decimals. Get ready to bust out those long division skills!8.NS.A.28.NS.A.1RIT Range: > 231Practice simplifying expressions with multiple radical terms combined by addition, subtraction, multiplication, and/or division.Evaluate numerical expressions with rational exponents, and convert between equivalent forms of exponential and radical expressions.Evaluate numerical exponential expressions and simplify variable exponential expressions by using the properties of exponents.Evaluate numerical expressions and simplify variable expressions with mixed exponential and radical terms, by using the properties of exponents.HSN-RN.A.2HSN-RN.A.1 | HSN-RN.A.2 HSN-RN.A.1 | HSN-RN.A.2 HSN-RN.A.1 | HSN-RN.A.2 Add, subtract, m ulti ply, a nd divide square ro o ts. Fo r exam ple, simplify ??5 0- HSN-RN.A.2 ?? 3 2. 6+ | The Real and Complex Number Systems | Extend and Use Properties | RIT > 231The Real and Complex Number SystemsExtend and Use PropertiesStandards AlignmentRIT Range: > 231Determine whether an expression that is the combination of two rational/irrational numbers is rational or irrational itself.HSN-RN.B.3 Fo r exam ple, sim plify ??18 as 3 ??2.HSN-RN.A.2Evaluate numerical radical expressions and simplify variable radical expressions by using the properties of exponents.Evaluate numerical expressions with unit-fraction exponents or radicals, and convert between the two forms of representations.HSN-RN.A.1 | HSN-RN.A.2HSN-RN.A.1 | HSN-RN.A.2RIT Range: 231 - 234Properties of exponents8.EE.A.1The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: < 160Practice solving word problems by adding small numbers (numbers 10 or less).K.OA.A.2Practice counting by tens..A.1Practice finding missing numbers in a list of numbers between 0 and 100..A.1Practice solving word problems by subtracting small numbers (numbers 10 K.OA.A.2or less).RIT Range: 161-178Practice solving problems like 34+5 and 34+50.1.NBT.C.4 Practice adding 3 numbers. All numbers in these problems are 20 or less. 1.OA.A.2 Practice adding. All numbers in these problems are 20 or less.1.OA.C.6Practice adding and subtracting to solve word problems. Numbers used are 1.OA.A.120 or less.Practice solving more challenging word problems with addition and subtraction. Numbers used are 20 or less.Practice solving word problems by finding how many more (or fewer) objects there are. Numbers used are 20 or less.Practice solving more word problems by finding how many more (or fewer) objects there are. Numbers used are 20 or less.1.OA.A.11.OA.A.11.OA.A.1Practice solving problems like 34+1 and 34+10.1.NBT.C.4Practice solving problems like 24 + 45.1.NBT.C.46+ | The Real and Complex Number Systems | Perform Operations | RIT 161-178The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 161-178Practice breaking apart problems like 23+45 into problems like 20+40+3+5. 1.NBT.C.4 Practice finding missing numbers in a list of numbers between 0 and 120. 1.NBT.A.1 Practice adding numbers like 45+8.1.NBT.C.4Practice solving word problems by finding how many more (or fewer) objects there are. Each problem shows a diagram to help you.1.OA.A.1RIT Range: 179-191Regrouping: two-digit number minus one-digit number2.NBT.A.4RIT Range: 179-191Practice adding and subtracting numbers like 554 and 237 using a number line. All numbers are less than 1000.2.NBT.B.7Practice adding two-digit numbers. All numbers in these problems are 100 2.NBT.B.5or less.Practice adding and subtracting to solve word problems. These questions are result unknown or change unknown problems. Numbers used are 100 or less.Practice solving word problems with addition and subtraction. These questions are comparison problems including difference unknown, smaller value unknown, and bigger value unknown. Numbers used are 100 or less.Practice solving word problems with addition and subtraction. These questions are start unknown problems including add to and take from problems. Numbers used are 100 or less.2.OA.A.12.OA.A.12.OA.A.1Practice solving more challenging addition and subtraction word problems 2.OA.A.1with "more" and "fewer".€ ? M ult i-step pro ble ms are also included. Numbers used are 100 or less.Practice adding and subtracting numbers like 54 and 37 using a number line. Numbers used in these problems are all less than 100.2.NBT.B.7Practice solving problems like 344+20 and 344+200.2.NBT.B.7Practice solving problems like 243 + 452.2.NBT.B.7Practice breaking apart big addition problems using place value. For example, 234+567 is the same as 200+500+30+60+4+7.2.NBT.B.7Find the total value when given an amount of coins or dollars.2.MD.C.8 | 2.NBT.A.291503523685500Practice solving problems like "- 45 = 27" where you have to figure out2.OA.A.1the missing value in an addition or subtraction equation.Add and subtract lengths to solve word problems.2.OA.A.1Practice adding 2-digit numbers like 43+27 that have sums that are multiples of 10.2.NBT.B.56+ | The Real and Complex Number Systems | Perform Operations | RIT 179-191The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 179-191Practice adding two-digit numbers by making groups of ten.2.NBT.B.5 Practice telling which strategies work for adding two numbers within 100. 2.NBT.B.7 Practice counting by 100s.2.NBT.A.2Practice counting by 10s.2.NBT.A.2Practice counting by 5s.2.NBT.A.2Read and interpret picture graphs.2.OA.A.1Practice solving problems like 67-5 and 67-50.2.NBT.B.5 Practice subtracting. All numbers in these problems are 20 or less.2.NBT.B.5 Practice subtracting 2-digit numbers.2.NBT.B.5Practice subtracting 1, 10, or 100 from a number.2.NBT.B.7Practice solving problems like 452 + 241.2.NBT.B.7 Practice subtracting 1 or 10 from a 2-digit number (no regrouping).2.NBT.B.5 Practice solving problems like 45 - 24.2.NBT.B.5RIT Range: 192 - 203Basic division3.OA.A.4Multiplying 1-digit numbers3.OA.A.4RIT Range: 192-202Practice adding three-digit numbers. All sums are 1000 or less.3.NBT.A.2 | 4.NBT.B.4Practice changing the grouping of factors in multiplication problems and see how it affects the product.3.OA.B.5Divide by 1. Quotients are less than or equal to 10.3.OA.C.7Divide by 10. Quotients are less than or equal to 10.3.OA.C.7Divide by 2. Quotients are less than or equal to 10.3.OA.C.7Divide by 3. Quotients are less than or equal to 10.3.OA.C.7Divide by 4. Quotients are less than or equal to 10.3.OA.C.7Divide by 5. Quotients are less than or equal to 10.3.OA.C.7Divide by 6. Quotients are less than or equal to 10.3.OA.C.745021553848000Divide by 7. Quotients are less than or equal to 10.3.OA.C.76+ | The Real and Complex Number Systems | Perform Operations | RIT 192-202The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 192-202Divide by 8. Quotients are less than or equal to 10.3.OA.C.7Divide by 9. Quotients are less than or equal to 10.3.OA.C.7 Practice making groups of 10 and 100 while adding 3-digit numbers.3.NBT.A.2 Use visual models to understand division.3.OA.A.2Practice representing multiplication as equal groups, repeated addition, or 3.OA.A.1arrays.Multiply a 1-digit number by a multiple of 10.3.NBT.A.3Solve word problems with multiples of ten. Decompose multiples of ten to 3.NBT.A.3 multiply. Multiply 0 or 1 times a number less than or equal to 10.3.OA.C.7Multiply 2 times a number less than or equal to 10.3.OA.C.7Multiply 3 times a number less than or equal to 10.3.OA.C.7Multiply 4 times a number less than or equal to 10.3.OA.C.7Multiply 5 times a number less than or equal to 10.3.OA.C.7Multiply 6 times a number less than or equal to 10.3.OA.C.7Multiply 7 times a number less than or equal to 10.3.OA.C.7Multiply 8 times a number less than or equal to 10.3.OA.C.7Multiply 9 times a number less than or equal to 10.3.OA.C.7Practice skip counting to find a number on a number line with only two tick 3.OA.C.7 marks labeled. See the relationship between multiplication and division problems.3.OA.B.6Find both the multiplication and division equation that can be used to solve a word problem.3.OA.B.6Give your brain a workout with these challenge problems on rounding.3.NBT.A.1Practice rounding to the nearest ten and rounding to the nearest hundred on the number line.3.NBT.A.1Practice rounding to the nearest ten and rounding to the nearest hundred. 3.NBT.A.1Subtract with 2 numbers less than 1000.3.NBT.A.2 | 4.NBT.B.4Solve two-step word problems with addition, subtraction, multiplication, and division. Some questions include estimation. 3.OA.D.8RIT Range: 203-212Understanding place value4.NBT.A.16+ | The Real and Complex Number Systems | Perform Operations | RIT 203-212The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 203-212Practice adding fractions that have denominators of 10 and 100.4.NF.C.5Add two fractions with the like denominators.4.NF.B.3Practice adding three-digit numbers. All sums are 1000 or less.3.NBT.A.2 | 4.NBT.B.4Practice solving multiplication and division word problems. Some problems 4.OA.A.2 have remainders.Learn to cancel zeros when dividing numbers like 3000 and 50.4.NBT.B.6Rewrite multiplication equations as comparisons and comparisons as equations. 4.OA.A.1Identify composite numbers less than 100.4.OA.B.4Practice rewriting decimals as fractions. These problems use decimals with tenths and hundredths.Practice rewriting fractions as decimals. Fractions in these problems have denominators of 10 and 100.4.NF.C.64.NF.C.6Practice writing a fraction as a mixed number and vice versa.4.NF.B.3 Practice writing decimal numbers shown in grid diagrams.4.NF.C.6 Practice writing decimal numbers in word form and number form.4.NF.C.6 Graph tenths between 0 and 1 on the number line.4.NF.C.6Graph hundredths between 0 and 0.1 on a number line.4.NF.C.6Practice breaking apart (decomposing) some number of hundredths into tenths and hundredths.4.NF.C.5Practice dividing 2-, 3-, and 4-digit numbers by a 1-digit number.4.NBT.B.6 Practice finding remainders in division problems, like 247÷5.4.NBT.B.6 Decompose 3- and 4-digit dividends to divide them by a 1-digit divisor. 4.NBT.B.6 Practice finding remainders in small division problems, like 24÷5.4.NBT.B.6Practice making equivalent fractions by multiplying the numerator and denominator by the same number.4.NF.A.1Practice writing equivalent fractions with denominators of 10 and 100.4.NF.C.5Practice writing equivalent fractions with denominators of 10 and 100. These problems give you pictures to help you find the answer.4.NF.C.5Practice finding factor pairs for whole numbers.4.OA.B.4Practice these problems to see how decimals and fractions can represent the same number.4.NF.C.6Demonstrate understanding of factors and multiples.4.OA.B.46+ | The Real and Complex Number Systems | Perform Operations | RIT 203-212The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 203-212Solve word problems that involve converting between U.S. dollars and cents and converting U.S. dollars to other units of money, like pesos. Solve word problems to find what time an event occurred or how long an event lasted.4.MD.A.24.MD.A.2Practice breaking up big division problems into smaller, simpler problems.4.NBT.B.6Multiply 2- or 3-digit numbers by 1-digit numbers. No regrouping.4.NBT.B.5Multiply 3- or 4-digit numbers by 1-digit numbers. Regrouping (carrying) needed.4.NBT.B.5Multiply 2-digit numbers by 2-digit numbers. Regrouping (carrying) needed. 4.NBT.B.5Multiply a 1-digit number by a multi-digit number by decomposing the multi-digit number.4.NBT.B.5Select the equation that can be used to solve a word problem.4.OA.A.1Practice multiplication problems like 5x100=500.4.NBT.B.5Practice multiplication problems like 5x500=2500.4.NBT.B.5Use an area model to decompose factors and multiply.4.NBT.B.5 Use an area model to decompose the larger factor and multiply.4.NBT.B.5 Practice matching fraction diagrams to multiplication expressions.4.NF.B.4 Practice multiplying 2-digit multiples of 10, such as 50x70=3500.4.NBT.B.5 Identify prime numbers less than 100.4.OA.B.4Practice division problems that work out to multiples of ten. Example: 1200 ÷ 30 = 40.4.NBT.B.6Practice rounding whole numbers to the nearest hundred or thousand.4.NBT.A.3Solve a subtraction problem with two fractions with like denominators.4.NF.B.3Subtract with 2 numbers less than 1000.3.NBT.A.2 | 4.NBT.B.4Practice seeing how one whole-number-times-fraction problem is the same as another. Find equivalent multiplication expressions.4.NF.B.4Practice finding equivalent fractions. These problems show you pictures of 4.NF.A.1fractions to help you out.Practice solving division problems with 0s in the dividend (for example, 204÷4).4.NBT.B.6Practice solving division problems with 0s in the solution, or quotient.4.NBT.B.6RIT Range: 213-219Dividing whole numbers by unit fractions5.NF.B.7 | 5.NF.B.7b6+ | The Real and Complex Number Systems | Perform Operations | RIT 213-219The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 213-219Dividing unit fractions by whole numbers5.NF.B.7 | 5.NF.B.7aDividing unit fractions by whole numbers introduction5.NF.B.7 | 5.NF.B.7aDividing whole numbers by unit fractions introduction5.NF.B.7 | 5.NF.B.7bFraction multiplication as scaling5.NF.B.5bRIT Range: 213-219Add two numbers that are written to the ones, tenths, or hundredths place. Add two numbers that are either whole numbers or written to the tenths place value.5.NBT.B.75.NBT.B.7Practice adding fractions that have different denominators.5.NF.A.1Practice adding and subtracting mixed numbers with different denominators. No regrouping required.Challenge problems involving adding and subtracting fractions that have unlike denominators.Practice solving fraction addition and subtraction word problems. The fractions in these problems have unlike denominators.Practice adding and subtracting mixed numbers with different denominators. Regrouping required.5.NF.A.15.NF.A.15.NF.A.25.NF.A.1Add tenths like 0.7 + 0.55.NBT.B.7Add whole numbers and tenths like 4 + 5.75.NBT.B.7Add larger numbers with tenths like 40.1+7.65.NBT.B.7Add whole numbers, tenths, and hundredths like 60+2.57 or 5.53+3.15.NBT.B.7Add more challenging whole numbers, tenths, and hundredths like 5.7+4.51 or 47.75+11.985.NBT.B.7Add hundredths like 0.76+0.215.NBT.B.7Divide numbers like 105÷21 or 119÷175.NBT.B.6Divide two whole numbers to get a quotient with a decimal.5.NBT.B.7Divide a whole number by a number written to the tenths or hundredths place. Quotients are whole numbers. Divide a whole number by a number written to the tenths or hundredths place. Quotients may include decimals.Divide two numbers. Divisors, dividends, and quotients can include decimals written to the tenths or hundredths place. 5.NBT.B.75.NBT.B.75.NBT.B.7Divide numbers like 2400÷30.5.NBT.B.66+ | The Real and Complex Number Systems | Perform Operations | RIT 213-219The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 213-219Dividing whole numbers to get a decimal quotient like 15÷6=2.55.NBT.B.7 Dividing decimals by whole numbers like 2.5÷5 or 1.86÷25.NBT.B.7 Dividing decimals where we can factor a 10 out of the divisor like 9÷30 5.NBT.B.7Dividing larger whole numbers by whole numbers to get a decimal like 80÷2005.NBT.B.7Dividing tenths by tenths like 0.6÷0.2.5.NBT.B.7Dividing numbers by 0.1 or 0.01 like 10÷0.1 or 5.3÷0.015.NBT.B.7 More challenging division with decimals like 14÷0.7 or 1.32÷0.12.5.NBT.B.7 Divide 3-digit and 4-digit numbers by a 2-digit number without remainders. 5.NBT.B.6Practice multiplying and dividing decimals by 10, 100, and 1000. For example, divide 31.4 by 100 to get 0.314.5.NBT.A.2Practice multiplying and dividing whole numbers by 10, 100, and 1000.5.NBT.A.2Multiply 2-3 digits by 3-4 digits with carrying.5.NBT.B.5Multiply a whole number times a decimal written to the tenths or hundredths place. Multiply two numbers. Factors are written to the ones, tenths, or hundredths place. 5.NBT.B.75.NBT.B.7Practice multiplying two fractions.5.NF.B.4Practice multiplying mixed numbers.5.NF.B.4Practice multiplying and dividing by powers of 10.5.NBT.A.2Practice multiplying and dividing decimal numbers by 10.5.NBT.A.2Multiply numbers like 900 x 10005.NBT.B.5Multiply tenths like 0.6 x 0.45.NBT.B.7Multiply decimals and whole numbers like 8x0.2 or 0.56x45.NBT.B.7 Multiply numbers with tenths and hundredths like 3.1x3.3 or 1.7x0.125.NBT.B.7 Solve and interpret fraction multiplication word problems.5.NF.B.6Practice evaluating powers of ten.5.NBT.A.2Round decimals and whole numbers to the nearest thousand, hundred, ten, one, tenth, or hundredth.5.NBT.A.4Round decimals using number lines. Select numbers that round to a given 5.NBT.A.4value.Practice using a number line to round decimal numbers.5.NBT.A.46+ | The Real and Complex Number Systems | Perform Operations | RIT 213-219The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 213-219Complete subtraction problems where both numbers are written to the hundredths place. Complete subtraction problems where both numbers are written to the tenths place. 5.NBT.B.75.NBT.B.7Practice subtracting fractions that have different denominators.5.NF.A.1Subtract tenths like 0.9-0.75.NBT.B.7Subtract small whole numbers and tenths like 1.6-0.35.NBT.B.7Subtract larger whole numbers and tenths like 78.4-35.NBT.B.7Subtract trickier numbers with tenths like 56.8-17.95.NBT.B.7Subtract hundredths like 0.75-0.565.NBT.B.7Subtract small whole numbers, tenths, and hundredths like 0.6-0.43 or 1.58-0.5 Subtract larger whole numbers, tenths, and hundredths like 67.89-6 or 35.65-17.34More challenging subtraction problems with whole numbers, tenths, and hundredths like 15-7.45 or 12.19-7.68Give the number of tens a number is being multiplied or divided by when the decimal is moved to the left or right.5.NBT.B.75.NBT.B.75.NBT.B.75.NBT.A.2Practice understanding that the fraction bar really means division.5.NF.B.3Practice word problems that involve using the fraction bar as division.5.NF.B.3Use area models, number lines, and tape diagrams to multiply a whole number times a fraction.5.NF.B.4Use area models and tape diagrams to multiply a fraction times a fraction. 5.NF.B.4Practice adding and subtracting fractions that have different denominators. Problems have fraction diagrams.5.NF.A.1RIT Range: 220-223Practice solving word problems by adding or subtracting decimal numbers. 6.NS.B.3Practice adding two numbers that are written to the tenths, hundredths, or thousandths place.6.NS.B.3Practice applying the distributive property to factor numerical expressions 6.NS.B.4(no variables).Practice dividing decimal numbers using "long division".6.NS.B.3Practice dividing fractions by fractions. No negative numbers are used in this exercise.6.NS.A.1Practice solving word problems by dividing fractions by fractions.6.NS.A.16+ | The Real and Complex Number Systems | Perform Operations | RIT 220-223The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 220-223Practice dividing multi-digit whole numbers. These problems use remainders.6.NS.B.2Solve word problems where you either need to find the GCF or LCM.6.NS.B.4Find the greatest common factor of 2 or 3 integers.6.NS.B.4Find the lcm (least common multiple) of pairs of integers.6.NS.B.4Practice multiplying two numbers that are written to the tenths, hundredths, or thousandths place.Practice subtracting two numbers that are written to the tenths, hundredths, or thousandths place.6.NS.B.36.NS.B.3Understanding dividing fractions by fractions6.NS.A.1RIT Range: 224-227Practice adding and subtracting positive and negative fractions.7.NS.A.1 Practice subtracting positive and negative single-digit numbers.7.NS.A.1 Practice adding positive and negative single-digit numbers.7.NS.A.1Practice solving word problems with negative numbers.7.NS.A.1 Practice comparing decimals, percents, fractions, and mixed numbers.7.NS.A.2 Practice simplifying complex fractions.7.NS.A.3Practice converting a fraction to a decimal.7.NS.A.2Practice dividing mixed numbers. Numbers in these problems may be positive or negative.Practice raising positive and negative numbers (integers only) to whole number powers. Watch out for mischievous negative signs that aren't really part of the base!Practice raising fractions to whole number powers. Fractions in these problems may be positive or negative.7.NS.A.27.NS.A.27.NS.A.2Practice classifying numbers as whole, integer, rational, and irrational.7.NS.A.3Practice finding the missing value in an addition or subtraction equation involving negative numbers.7.NS.A.1Practice solving addition and subtraction problems with negative numbers. 7.NS.A.1Practice plugging in values to evaluate negative number addition and subtraction expressions.7.NS.A.1Practice multiplying and dividing integers.7.NS.A.2Practice writing addition and subtraction equations to match number line diagrams.7.NS.A.16+ | The Real and Complex Number Systems | Perform Operations | RIT 224-227The Real and Complex Number SystemsPerform OperationsStandards AlignmentRIT Range: 224-227Practice identifying equivalent expressions involving the addition and subtraction of negative numbers.Practice matching addition and subtraction equations to real-world scenarios.7.NS.A.17.NS.A.1Practice matching situations to multiplication and division expressions and 7.NS.A.2equations.Practice evaluating expressions using the order of operations. Numbers used in these problems may be negative.Practice determining whether the sum of two numbers is positive, negative, or zero. Practice working through addition and subtraction problems using the number line.Practice solving challenging negative number addition and subtraction problems. Number line models, variables, and absolute value come together to push your knowledge of negative numbers even deeper (maybe even below zero!).7.NS.A.27.NS.A.17.NS.A.17.NS.A.1RIT Range: > 231Practice addition and subtraction with complex numbers.HSN-CN.A.2Simplify expressions with base i (the imaginary unit) raised to a positive exponent.Multiply complex numbers by single terms that are either real or pure imaginary.HSN-CN.A.1 | HSN-CN.A.2HSN-CN.A.2Given two complex numbers, find their product.HSN-CN.A.2 Determine the real and the imaginary parts of complex numbersHSN-CN.A.1 Rewrite square roots of negative numbers as imaginary numbers.HSN-CN.A.1 Classify numbers as real, pure imaginary, or complex.HSN-CN.A.1Determine the appropriate unit of a quantity based on a formula containing that quantity.The Real and Complex Number SystemsRatios and Proportional RelationshipsHSN-Q.A.1Standards AlignmentRIT Range: 203-212Multi-step word problems with whole numbers4.OA.A.3RIT Range: 203-2126+ | The Real and Complex Number Systems | Ratios and Proportional Relationships | RIT 203-212The Real and Complex Number SystemsRatios and Proportional RelationshipsStandards AlignmentRIT Range: 203-212Practice converting a US customary measure of volume to a smaller unit. 4.MD.A.1 Practice converting a metric measure of mass to a smaller unit.4.MD.A.1 Practice converting a US customary measure of length to a smaller unit. 4.MD.A.1 Practice converting a metric measure of volume to a smaller unit.4.MD.A.1 Practice converting a metric measure of length to a smaller unit.4.MD.A.1 Practice converting a US customary measure of mass to a smaller unit. 4.MD.A.1 Practice estimating the volume of real life objects using US customary 4.MD.A.1 Practice converting a measure of time to a smaller unit.4.MD.A.1Solve word problems that involve converting between U.S. dollars and cents and converting U.S. dollars to other units of money, like pesos. Solve word problems to find what time an event occurred or how long an event lasted.Practice estimating the length of an event using seconds, minutes, and hours.4.MD.A.24.MD.A.24.MD.A.1RIT Range: 213-219Solve word problems that involve converting between metric measures of 5.MD.A.1distance, volume, and mass, as well as measures of time.Convert between metric measures of distance, volume, and mass.5.MD.A.1Convert between US customary measures of distance, volume, and mass.5.MD.A.1Solve word problems that involve converting between US customary measures of distance, volume, and mass.5.MD.A.1RIT Range: 221 - 22591948024511000Units6.RP.A.3 | 6.RP.A.3dRIT Range: 220-223Example problem: Three different stores are offering a deal on pencils. Which store has the lowest price per pencil?Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent.6.RP.A.2 | 6.RP.A.36.RP.A.3Practice solving word problems involving percents.6.RP.A.3Use rates to solve word problems. For example, Charlie can type 675 words in 9 minutes. How many words can Charlie type in 13 minutes?6.RP.A.2 | 6.RP.A.36+ | The Real and Complex Number Systems | Ratios and Proportional Relationships | RIT 220-223The Real and Complex Number SystemsRatios and Proportional RelationshipsStandards AlignmentRIT Range: 220-223Practice solving ratio word problems like, "If Ben reads 10 pages in 15 minutes, how long does it take him to read 40 pages?"Choose the ratio that goes with a picture of two quantities like apples and bananas. 6.RP.A.36.RP.A.1Practice filling out tables of equivalent ratios.6.RP.A.3RIT Range: 224-227Practice telling whether or not the relationship between two quantities is proportional by reasoning about equivalent ratios.Practice telling whether or not the relationship between two quantities is proportional by looking at a graph of the relationship.7.RP.A.27.RP.A.2Practice setting up and solving proportions to solve word problems.7.RP.A.3Practice solving word problems involving price discounts, taxes, and tip calculations.7.RP.A.3Practice reading and analyzing graphs of proportional relationships.7.RP.A.2Practice solving word problems involving price markups and commission fees.7.RP.A.3Practice solving basic proportions.7.RP.A.3Practice computing rates associated with ratios of fractions or decimals.7.RP.A.1 | 7.RP.A.2Practice writing proportions to describe real-world situations.7.RP.A.3Practice writing equations to describe proportional relationships.7.RP.A.2 ................
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